ADVANCES IN ONTOLOGIES

Proceedings of the Sixth Australasian Ontology Workshop Adelaide, Australia, 7 December 2010

Sponsored by the International Association for Ontology and its Applications http://www.iaoa.org

Kerry Taylor, Thomas Meyer and Mehmet Orgun, Editors

Preprint. To be published as Vol 122 in the Conferences in Research and Practice in Information Technology Series by the Australian Computer Society Inc. http://crpit.com/

Preface

The series of Australasian Ontology Workshops, begun in 2005, is now in its sixth year with the Australasian Ontology Workshop (AOW 2010), to be held at the University of South Australia (City West Campus), in Adelaide, Australia on the 7th December 2009. Like most of the previous workshops, AOW 2010 is held in conjunction with the Australasian Joint Conference on Artificial Intelligence, now in its 23rd year as AI10.

We welcome, for the first time, the sponsorship of AOW by the International Association for Ontology and its Applications (IAOA). It is a non-profit organisation established in 2010 to promote interdisciplinary research and international collaboration at the intersection of philosophical ontology, linguistics, logic, cognitive science, and computer science, as well as in the applications of ontological analysis to conceptual modeling, knowledge engineering, knowledge management, information-systems development, library and information science, scientific research, and semantic technologies in general.

Our invited keynote speaker, Professor Riichiro Mizoguchi, is a member of the executive council of IAOA, and is based at the Institute of Scientific and Industrial Research at Osaka University, Japan. He has analysed the well-known upper ontologies and finds them lacking in three areas of great importance to e-research and interoperability: quality, representation, and process/event. He will present an alternative ontology, called YAMAMOTO at AOW 2010.

Out of ten papers submitted to AOW 2010, we accepted eight on the basis of three or four reviews each of full papers by our program committee of international standing. Our papers offer a balance of topics that has become typical for AOW: four quite theoretical, one about practical general-purpose tools, and two using ontologies together with other tools to solve application problems. Despite being a nationally-titled workshop, located with a national conference, we were very pleased to note the truly international nature of our submitting authors: from France, Germany, US, Canada, and Japan as well as Australia.

For the second time this year, AOW is awarding a best paper prize. The winner will be announced at the workshop. Also, extended forms of selected papers from the workshop will be invited for inclusion in a forthcoming Springer book.

Many individuals contributed to this workshop. We thank our contributing authors and our invited speaker, Riichiro Mizoguchi, who is travelling to Australia especially for this event. We thank our international Program Committee and additional reviewers for their careful reviews in a tight time-frame. We appreciated the support of the organising committee for AI10, most especially the Organising chair, Ivan Lee and the Workshops chair Dianhui Wang.

We acknowledge the EasyChair conference management system which was used in all stages of the paper submission and review process and also in the collection of the final camera-ready papers. We thank Vladimir Estivill-Castro and Simeon Simoff, the editors of the CRPIT series, for facilitating the formal publication of the AOW 2010 proceedings, and Ivan Lee for organising pre-prints for the day of the workshop.

We hope that you find this Sixth Australasian Ontology Workshop to be informative, thought-provoking, and most of all, enjoyable!

Thomas Meyer, CSIR Meraka Institute, South Africa

Mehmet Orgun, Macquarie University, Australia

Kerry Taylor, CSIRO ICT Centre, Australia

Chairs of AOW 2010

December, 2010

Conference Organisation

Programme Chairs

Thomas MeyerMehmet OrgunKerry Taylor

Programme Committee

Franz BaaderArina BritzWerner CeustersMichael ComptonOscar CorchoR. Cenk ErdurAurona GerberDennis HooijmaijersTertia HorneBo HuRenato IannellaKen KaneiwaC. Maria KeetKevin LeeLaurent LefortConstantine MantratzisLars MoenchDeshendran MoodleyMaurice PagnuccoDebbie RichardsRolf SchwitterMurat SensoyMarkus StumptnerBoontawee SuntisrivarapornSergio TessarisNwe Ni TunIvan VarzinczakKewen WangAntoine Zimmermann

Table of Contents

YAMATO: Yet Another More Advanced Top-level Ontology (invited talk) 1Riichiro Mizoguchi

A Visual Analytics Approach to Augmenting Formal Concepts withRelational Background Knowledge in a Biological Domain . . . . . . . . . . . . . . 17

Elma Akand, Michael Bain, Mark Temple

Combining Ontologies And Natural Language . . . . . . . . . . . . . . . . . . . . . . . . 27Wolf Fischer, Bernhard Bauer

Comparison of Thesauri and Ontologies from a Semiotic Perspective . . . . . 35Daniel Kless, Simon Milton

Fast Classification in Protege: Snorocket as an OWL2 EL Reasoner . . . . . 45Michael Lawley, Cyril Bousquet

Ontological Support for Consistency Checking of Engineering DesignWorkflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Franz Maier, Wolfgang Mayer, Markus Stumptner

Ontology Inferencing Rules and Operations in Conceptual StructureTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Philip H.P. Nguyen, Ken Kaneiwa, Minh-Quang Nguyen

An Axiomatisation of Basic Formal Ontology with Projection Functions . 71Kerry Trentelman, Barry Smith

Making Sense of Spreadsheet Data: A Case of Semantic Water DataTranslation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Yanfeng Shu, David Ratcliffe, Geoffrey Squire, Michael Compton

YAMATO: Yet Another More Advanced Top-level Ontology

Riichiro Mizoguchi The Institute of Scientific and Industrial Research

Osaka University 8-1 Mihogaoka, Ibaraki, Osaka 567-0047 Japan

miz@ei.sanken.osaka-u.ac.jp

Abstract Upper ontology plays a critical role in ontology development by giving developers a guideline of how to view the target domain. Although some upper ontologies such as DOLCE, BFO, GFO, SUMO, CYC, etc. are already developed and extensively used, a careful examination of them reveals some room for improvement in a couple of respects. This paper discusses YAMATO1: Yet Another More Advanced Top-level Ontology which has been developed intended to cover three features in Quality description, Representation and Process/Event, respectively, in a better way than existing ontologies.

Keywords: Upper ontology, Ontological engineering, quality and quantity, informational objects

1 Introduction Upper ontology is the key of ontology engineering. It plays a critical role in ontology development by giving developers a guideline of how to view the target domain. There already exist beautifully designed upper ontologies such as DOLCE(Guarino 2010), BFO(Smith 2010), GFO(Herre 2010), SUMO(Pie 2010), CYC(Lenat 2010), etc. It seems there is no need to develop yet another upper ontology. However, careful examination of them reveals some room for improvement in three respects: (1) Quality and quantity, (2) Ontology of representation, and (3) Distinction between processes and events.

First, quality and quantity need more careful investigation. One of the most sophisticated property ontologies is found in DOLCE. It specifies value space for each quality type under the name of Quality space(region). A remarkable feature of DOLCE’s conceptualization about it is the clear distinction between the quality an object possesses and the quality value(quale/qualia) itself. This feature is good to support description using <Entity, Attribute Value> triple2 (referred to as <E, A, V> triple hereafter) which has been used in knowledge representation in AI. However, there are other ways of quality description such as <patient_1, diarrhea>, <cupper, conductive>, and <rose_1, redness, faint> which seem not to be covered by DOLCE’s quality ontology. On the other hand, BFO’s quality ontology has been obtained under the principle of simple and capturing essentials of quality and

1 YAMATO is the next version of YATO and the name was suggested by Peter Simons who loves the Japanese battle ship “Yamato”. Yamato is also the name of the oldest Japanese government. 2 In AI, “Object” is used instead of “Entity”, but to extend the target things to be described to occurrent, I use “Entity”.

covers only <Entity, Property> type description. As far as I know, there exist three kinds of data description such as <E, A, V>, <E, P> and <E, P, V> (Egana 2008). However, there is no ontology which supports all these three kinds of quality descriptions. Even worse, no existing upper ontology distinguishes between quality in reality and quality description, which causes some confusion when talking about quality and quantity. The author believes quality ontology should contribute to facilitation of data interoperability as well as capturing quality ontologically.

The second aspect is informational object. There are a lot of informational objects in the world: documents, books, music, Web pages, etc. They are different from ordinary things in that they have content, that is, they are “content-bearing things”, while cars, tables, dogs, trees are not. Because representation-related things are classified as semiotics, it has not been discussed in the philosophical ontology very well. However, we need an ontology of informational object from the ontological engineering point of view. Ontology of informational object is discussed extensively in DOLCE D&S(Gangemi 2003) and SUMO. Although these ontologies contribute to better understanding of informational object, there is some room for improvement. One aspect is the clear differentiation between representation and representing things together with its elaboration. For example, while a book as representing thing is, say, a book you buy at a book store, a book as representation is what the author wrote, that is, something left after subtracting sheets of paper from the book you buy. It should also be the book in a CD-ROM. In addition, I believe finer-granular types for talking about informational object are needed. DOLCE D&S has rich conceptualization about representation. It incorporates situation and concept to realize very comprehensive ontology of representation. Although it is sophisticated, the framework introduced is a bit too large to deal with ordinary informational object such as sentence, music, plan, etc. Especially, situation is not necessary to talk about representation. What is more problematic is introduction of definition of a concept into ontology because as discussed in Section 4, it violates the principle “Theory shouldn’t talk about itself in it” (See 4.1).

The third aspect is most fundamental and is related to differentiation among objects, processes and events. There are several views about them. The typical ones are 3D view and 4D views. BFO nicely reconciles the two views by introducing SNAP and SPAN ontologies. GFO is based on 4D view. DOLCE is based on 3D view. Although discussion on difference between objects, processes and events are made in these ontologies, what can change and what is an object at all are not very clear. I see both 3D and 4D views of the world are incorrect. I could say the idea of neither “objects prior to processes” nor “processes prior to

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objects” is correct, but both are mutually dependent. Furthermore, processes can change, though events cannot(Galton 2009).

This paper discusses a new upper ontology called YAMATO: Yet Another More Advanced Top-level Ontology developed to cover the above three issues which the existing upper ontologies fail to explain satisfactorily. YAMATO is not fully axiomatized yet, though it should be done in the near future. It is implemented in Hozo and OWL and open for use at http://www.ei.sanken.osaka-u. ac.jp/hozo/onto_library/upperOnto.htm. Some might see YAMATO is too large and complex. I believe such a criticism does not apply to YAMATO which tries to reveal secrets of reality as fine as possible under the condition of maximization of its utility in practice. Many of the existing upper ontologies are too simple to explain the reality and to guide domain people to build their ontologies. What they need are not only distinction between objects and qualities but also that between quality and quantity and that between quality and description of quality, not only that between objects and representation but also that between a copy of book and book and that between a novel and a musical score, and not only that between process and event but also that between a pulse and a sequence of pulses and that between to grow and to cut, etc. They also need to know how much similar a procedure and a piece of music are in what sense, why events cannot change while processes can, etc. YAMATO is designed to answer all the above questions and the like.

2 Overview of YAMATO

2.1 Basic definitions Ontology design is a kind of design activity which necessarily has some design rationale that largely influences the resulting ontology. In the case of BFO, it is “representation of reality”, for example. In other words, any ontology cannot be free from some assumption and/or designer’s standpoint. The standpoint taken in YAMATO consists of Newtonian world point of view and 3D-like modeling, that is, the world is considered as being composed of the three-dimensional Euclidean space with the absolute time and both object(continuant) and process (occurrent) exist with equal importance in a mutually-dependent manner which is discussed in detail in (Galton 2009). Furthermore, we do not go into micro-level world in which we need to talk about atoms and/or particles. By water, I mean amount of water rather than H2O, since we need to say water is dissective. If we take H2O into account, it is apparently not dissective. This premise is necessary to build a consistent ontology. The following list includes basic distinctions made in YAMATO. (1) Substrate and entity

Space and time are indispensable for things to exist in the world, while these two can exist independently of entities. Such independence is essential and differentiates the two from entities that inherently need these two to exist in the real world. Matters are less basic than space and time, but it still is very substrate-like because every physical individual is made of/from matter.

(2) Entity and property

Any entity cannot exist without any property, e.g., any physical object has necessarily a couple of properties (color, mass, size, etc.). At the same time, any property cannot exist alone. It necessarily needs an individual to inhere in. Thus, both an individual and a property are inherently dependent on each other and cannot be separated. Such a deep mutual independence is an essential structure of being: objects vs. processes and matter vs. physical objects are other examples, though kinds of dependency are different from each other.

(3) Physical and abstract We define a physical thing as something which needs time and space to exist, and introduce semi-abstract which needs only time to exist. Needless to say, there is nothing which requires only space to exist. Abstract things are defined as things that need neither time nor space.

(4) Continuant(Object) vs. Occurrent(Process3) This is one of the most controversial issues and has a long history of debate. It is sometimes called 3D model vs. 4D model. Common sense is based on 3D model which consists of the 3D Euclidean space with absolute time. YAMATO is based on a solid theory of objects, processes and events, and it deals with them of equal importance (Galton 2009). Furthermore, it clearly identifies events are made of processes and while processes can change, events cannot. We do not use the term “perdurant” for explaining processes because it blocks to talk about the difference between processes and events.

(5) Entity and relation Relation is sometimes considered as abstract. But it is not true, though it is something in the higher order than an entity, that is, entities first exist and relations are something found between entities. An example is the marital-relation with Mr. A and Ms. B that is time-dependent and hence cannot be abstract. Although it is intangible, it exists in the time frame of the real world. Friendship between persons, marital relation, part-whole relation, etc. exist in the world. People sometimes confuse relation as a formalism with relation as an existing thing. Typical examples are action and attribute that are sometimes formalized as a relation because an action is often formalized as one between an actor and an object and an attribute as one between an object and a value. But, of course, they are not relations ontologically. They are intrinsically entities included in an ontology.

(6) Informational object vs. non-informational object (Representation and non-representation)

Informational object and symbols are usually dealt with in semiotics rather than in ontology. However, from the real-world modeling point of view, we need to deal with informational object in our ontology, since there apparently exist music, novels, texts, symbols and so on in the real world. Informational object and non-informational object (object, process,

3 Before coming to the discussion on the difference between processes and events, by the term process, we mean “occurrent”.

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relation, attribute, etc.) are very different from each other. For the informational object, it is not easy to identify what their instances are. For example, what an instance of a piece of music is, what an algorithm is, how both are similar ontologically, etc. need some in-depth consideration.

2.2 Top-level categories YAMATO adopts single inheritance to make the taxonomic structure clean like BFO and DOLCE. Using is-a relation, it is realized in YAMATO that the type hierarchy is made only when the lower type inherits its intrinsic properties from the super types. Many of the multiple context-dependencies are covered using roles (Mizoguchi 2007). For the cases where genuine multiple inheritance is necessary, Hozo (Kozaki 2010) prepares IS-A relation which is nothing to do with identity problem of instances but only with property inheritance. It is allowed to use only when is-a relation already exists between the two types of interest. The early version of YAMATO has been designed under a considerable influence of Guarino’s upper ontology (Guarino 1995). is-a relation in YAMATO is something more than usual property inheritance. That is, it implies inheritance of identity criterion, so that when an instance of such a class loses the essential property, then it stops being an instance of all its super classes. On the other hand, whatever happen with such properties of an instance that are inherited through IS-A relation, no influence occurs concerning the identity of the instance. Note that a type is not a property in YAMATO. Therefore, human is a type and is not dealt with as a property. Instead, human type has properties/qualities such as height, weight, age, etc4.

Fig. 1 shows the top-level categories of YAMATO. At this level, YAMATO has little significant difference from other existing ontologies. A more finer-grained view of YAMATO is shown in Fig. 2 that reveals its features. It shows a clear distinction between process(a) and event(b).

4 Terminological issues about property and quality is discussed in 3.2.6 extensively.

Concerning ontology of representation, representing thing(d5) is classified under artifact(c), while content(f) and representation(g) are classified under semi-abstract(e) because it needs only time to exist. Quality_quantity(h) is divided into quality value(i) and quality(l). The former has categorical(j) and quantity(k) as its subclasses and the latter generic quality(n) and property(m). The details are discussed in the following sections.

3 Quality and Quantity

3.1 Background e-Science needs data exchange world-wide. Especially, in biology and bio-informatics, data exchange has been intensively conducted through global collaboration in the daily activities. In order to make it smooth to exchange scientific data, the way of description must be compatible with each other. Description of data/objects is usually done by determining attribute values. However, quality

5 In the ontology “represented thing” which should be “representing thing” still remains.

(a)(b)

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Fig. 2 Detail version of top-level categories.

Fig. 1 Top-level categories.

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description is not well-understood by practitioners. Even professionals seem not to agree on the common way of quality description of objects. This is why in OWL best practice WG, there proposed several patterns which would be useful in many cases of quality description.

As is discussed in (Egana 2008), there are at least three ways of quality description recommended by BFO, DOLCE and Galen(Alan 2010). BFO recommends <Entity, Property> (e.g., <John, tall>) formalism, while DOLCE <Entity, Attribute, Value>(e.g., <John, height, 180cm>) and Galen <Entity, Property, Value>(e.g., <John, tallness, large>6). The problem is two fold: (a) one way of representation is not enough for real world problems because there exist multiple kinds of quality descriptions in the real data and (b) there is no explicit model of how these three are different from and interrelated with each other. The ontology of Quality and Quantity in YAMATO tries to give fundamental conceptualization of those existing descriptions in one ontology. To do so, YAMATO distinguishes between quality in reality and quality description and has a type hierarchy which reflects existing notions used in quality descriptions.

Another problem is that there exist several ways of implementation of a formulation. In OWL, attribute is usually represented in object property. That is, (Entity --attribute--> value) in which attribute is not dealt with as an entity but as a relation. This implementation fails to appropriately represent the growing boy discussed below. It suggests that not only ontology but tools supporting the ontological formulation are also key factors of successful data description. Note here that Hozo(Kozaki 2010), the tool our group has been developing, is compliant with YAMATO proposed in this paper.

3.2 Quality

3.2.1 The underlying philosophy One of the contributions of our ideas is clear distinction between attribute and attribute values. As far as I know, there are three dependent entities related to the term attribute: (1) attribute as a type that plays as dimension, (2) attribute as an instance and (3) attribute value that might correspond to quantity. However, some ontologies do not distinguish between (2) and (3). In this respect, DOLCE nicely differentiates instance of attribute from attribute value by introducing quality for attribute as an instance and quale/qualia for attribute value. This differentiation enables us to capture a thing, holding a quantity(qualia), that can change keeping its identity as we discuss it below. In other words, any quantity exist only one in the world

6 A better example would be <John, diarrhea, severe>.

independently of how many things have those quantities as their values. We build an ontology for each of attribute(generic quality) and attribute value(quantity) intended to describe things in terms of the combination of those dependent entities. We discuss each of the two in turn.

3.2.2 An example See Fig. 3 that shows an example of quality which I believe many people can agree that it is an example of quality. The issue here is how to wisely model this quality. Fig. 3 also shows types and individuals underlying the quality. Among them, “John”, “160” and “cm” have no issue to discuss. Let us briefly investigate characteristics of the others. Firstly, “John’s height” is something associated with John and exists at the instance level. “Height” is generic in the sense that the entity which it is associated with is unspecified, but is more specific than “length” in the sense that it is dependent on what to measure and how. This suggests the notion of “quality role” played by length, which is an interesting topic, but it will be discussed later. The “length” is quite generic because it can be height, depth, distance, etc. according to the context and exists at the class level. Finally, “160cm long” seems to be quantity and exists at the instance level. In summary, issues include (1) if “160cm long” is a quality or a quantity, (2) if an instance of a quality is a quantity or not, (3) what is “John’s height”?, (4) what is “height”?, and (5) how is “length” different from “height”? The following subsections are devoted to answer these questions.

3.2.3 On change See Fig. 4 that shows a boy named John who grows. His

height was 160cm in 2008 and 170cm in 2009. Ontologically, in order to talk about change properly, we need a non-changing thing keeping its identity during the change process, otherwise, there cannot exist a change but just a difference. In the case of growing John, John and his

Quality: John’s height of 160cm long

John, John’s height, height, length, 160cm long, 160, cm

Object/humanObject/human Associatedwith JohnAssociatedwith John

Dependent onthe way ofmeasuring

Dependent onthe way ofmeasuring

QuitegenericQuitegeneric

lengthquantitylengthquantity

numbernumber Unit/dimensionUnit/dimension

Fig. 3 An example of quality.

160cm170cm

In quantity space,they have

different ID

As quality,they shareSame ID

2008 2009

160cm170cm

In quantity space,they have

different ID

As quality,they shareSame ID

2008 2009 Fig. 4 A growing boy and his height quality.

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height must keep their identities. That is, “John’s height” must have the same identity at the times of 2008 and 2009. The values, on the other hand, are 160cm in 2008 and 170cm in 2009, respectively, and they have their own different identity. This analysis reveals that “John’s height” has something having its identity and it is generic in the sense that its possible values are indefinite.

3.2.4 Quality role We here discuss the notion of quality role. Many of the qualities people know are not basic quality7 but quality role. Let us take an example of height. It is a quality role whose basic quality is length. In the role theory (Mizoguchi 07), it can be said that “height role is played by length in the context of a human body”. Height is what is measured in the direction roughly along the vertical axis from the ground level to the top. Similarly, depth, width and distance are quality roles played by length as well. It is just like a man plays a husband role when he has got married and like a human plays a teacher role in the context of a school. Let us call quality such as length as basic quality temporarily. Examples of basic qualities include length, area, mass, temperature, flow rate, voltage, etc. Basic qualities are context-independent and intrinsically represent kinds of quality, and roughly equal to physical dimensions. Quality roles include height, depth, input flow rate, maximum weight, area of cross section, etc. Table 1 shows examples of quality roles.

Table 1 Some quality roles.

Quality role Basic quality

Quantity (number +

unit)

age years integer + year

height length real + m

width length real + m

distance length real + m

area of cross section

area real + m2

input flow rate flow rate real + m3/hour

The notion of quality role satisfies context-dependence

which is one of the most important properties of roles. In the case of teacher role, a school is its context in which teacher role is defined. In the case of height, which is a quality role played by length, on the other hand, its context

7 This term is temporary and will be renamed as generic quality type later.

would be human body, building, etc. with the measuring manner from the ground level to its top.

3.2.5 Summary of the discussion on quality A quality must be a certain dependent property possessed by an entity and keeps its identity while its value changes. In the case of growing John, this understanding suggests that not “John’s height of 160cm long” but “John’s height” should be taken as a quality as shown in Fig. 5. As is already clear, quality roles are necessarily associated with a particular entity which is the context of them at the instance level. The fact satisfies the requirement of quality. Therefore, quality roles are what should be called quality. Then, “John’s height of 160cm long” would be called quality instance8 because it is a realization of quality role “John’s height” at a certain time. In terms of role theory, “John’s height of 160cm long” is called a role holder, which will be explained later, which means a length playing the “John’s height” role. Then, “height” is called quality role type which has “John’s height” as its instance and “length” should be called generic quality type because it is not associated with any entity yet and specifies what kind of quality there exist. It was called basic quality in the above. The results are summarized in Fig. 5. Definitions of these basic terms are shown in the following:

1. Generic quality type: The most generic property which is not yet associated with any particular context and can play quality role. It represents kinds of property at the class level and its instances represent concrete values corresponding to quantity to play quality role: e.g., length, weight, mass, color, area, flow rate, etc.

2. Quality role type: It is a type of property associated with a context, and hence is equal to quality role at the class level. Its instance is played by an instance of generic quality type: e.g., height, depth, (something’s) length, (someone’s) weight, mass of cross section, input voltage, etc.

3. Quality: It is a property associated with an individual entity and is a generic name to denote each instance of quality role type: e.g., John’s height, Tom’s weight, area of the cross section of this pipe, length of this pen, etc.

4. Quality instance: A realization of quality: e.g., John’s height of 160cm long, Tom’s weight of 50kg, etc.

These types and their relations are depicted in Fig. 6. Examples of relations between these types are shown

8 Although quality realization might be a better name, I use quality instance to minimize peculiarity.

John, John’s height, height, length, 160cm long, 160, cm

Object/human QualityQuality

role typeGenericquality

type

lengthquantity

number Unit/dimension

Quality instance: John’s height of 160cm long

John, John’s height, height, length, 160cm long, 160, cm

Object/humanObject/human QualityQualityQuality

role typeQuality

role typeGenericquality

type

Genericquality

type

lengthquantitylengthquantity

numbernumber Unit/dimensionUnit/dimension

Quality instance: John’s height of 160cm long

Fig. 5 Informal definitions of quality-related terms.

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below for further clarification: <“John’s height of 160cm long” realization-of “John’s

height”> <“John’s height” instance-of height> <”height” (role) is-a quality role type> <“height” (role) is-played-by length> <quality role type is-played-by generic quality type > <length is-a generic quality type> <160cm long instance-of length quantity> <length quantity is-a quantity>

Fig. 6 also shows two height quality values of John at times of 2008 and 2009. Although two height quality roles of John are shown, they share the same identity, while the two length quantities, 160cm and 170cm have their own identities.

I suspect readers would need an explanation about examples of “(something’s) length” and “(someone’s) weight”. Before explaining them, however, I need to explain role theory using Hozo way of representation of roles (Mizoguchi 2007). Fig. 7 shows Hozo legend of role definition in which front wheel role is defined in the context of bike. It says that a front wheel role of a bike must be played by a wheel, and front wheel which is a wheel playing a front wheel role is called role holder and defined as shown in Fig. 7. In the case of a pen, its length

role is played by length. Note here that the term “length” appears twice in the role name and in the role player name, which is the source of confusion. The former length is a type similar to height and depth because it is tightly associated with its context and the latter length means one-dimensional extent and is a type similar to area and voltage. This is why “(something’s) length” is dealt with a quality role type rather than generic quality type. Exactly the same applies to “(someone’s) weight”, too, that is, “(someone’s) weight” is a quality role played by an instance of weight as a generic quality type.

Height role holder of human type also needs an explanation. Height role of human is a type of height role of John and the former height is a quality role type and the latter height is a quality. These relationships are consistent with type-instance relation. On the other hand, however, it is not clear what is height role holder of human type. It is a type of J-height role holder of John in Fig. 6. At the same time, it looks like quality role type as well. This asymmetry comes from the nature of roles. We have no space to discuss this topic in detail, and I would like to discard what height role holder of human is and to leave the definitions as they are because height role of human has less association with “definite value” than height role holder of human.

Quality instance

Quality type

Genericqualitytype

Quantity Quantity (instance)

J-height

QualityQuality instance

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Quality type

Genericqualitytype

Quantity Quantity (instance)

J-height

QualityQuality instance

Quality type

Genericqualitytype

Quantity Quantity (instance)

J-height

Quality

Sharesame ID

Different ID

Fig. 6 Quality ontology and its use in Hozo (Rectangles with round corners denote instances).

Role concept

Role holder

Context

Role player

To be defined

Referring to the other type

To be defined

Role concept

Role holder

Context

Role player

To be defined

Referring to the other type

To be defined

Fig. 7 Hozo legend of role definition [Mizoguchi 2007].

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3.2.6 On terminology There exist similar terms such as property, attribute, quality, quality type, quality role type and quantity. All are dependent entities and cannot exist without an entity with which they are associated. It was almost impossible to define these terms without discussing deep issues related to them. Because of this difficulty, terms such as attribute and property used thus far should not be taken as technical terms but as common words which are vaguely defined. But, now it is the time to differentiate them based on our discussion thus far. Quality, quality role type and quantity are already defined with examples. So, the problem is the rest two. Therefore, these terms appearing below should be taken as defined here.

Property: As a common term, property is almost a synonym of quality in our context. As a technical term, however, they are different. The major difference is that while a property can be used as any predicate to any individual like human(x) or animal(x), quality is used only for what an entity has. However, considering that our problem in this paper is to talk about how to describe/characterize entities, property and quality become synonym again because there is no necessity for talking about “human as a property” when describing “human” entity. This definition is only valid in the following sections in this paper, that is, the term property appearing in the above should not be taken as defined here.

Because we defined quality differently from what is defined in BFO, by property, I mean “quality” used in BFO, that is, value combined with its variable or the variable taking a value that can be possessed by an entity. I think I need to defend my decision on this. Quality must be something associated with an entity and can change with keeping its identity. These characteristics necessarily derive that quality cannot be something combined with its value, otherwise, it cannot keep its identity when its value has changed. Therefore, the notion of quality employed in BFO is not appropriate in this respect. As was already discussed, an instance of BFO-defined quality such as “John’s height of 160cm long” is called quality instance and any length whose value is 160cm is represented as property in YAMATO, though property is defined mainly for qualitative property such as being red, being natural, being artificial, etc..

Attribute: Originally, it is a binary predicate which relates an entity to its quality instance, e.g., length(pen_1, 10cm). In AI, <E, A, V> is often used to describe entities. In such cases, “A” stands for quality role type and/or generic quality type. Following the use of this term in AI, we could define attribute as a synonym of generic quality type. However, we intentionally leave this term undefined for flexible use in text. So, the term attribute should be taken as a common term in this paper.

In YAMATO implemented in Hozo, the term property is used to mean BFO’s quality. Because the role hierarchy is implicit in Hozo, hierarchies of quality and quality role type are invisible unless Role hierarchy mode of Hozo is used.

3.3 Quantity

3.3.1 What is quantity? I understand there is a strong temptation to say that quantity is instance of quality. For example, “1m long” seems like an instance of length quality. At first glance, it looks true because it seems simple and natural. However, the facts that quantity must have its own subtype structure to represent quantized quantity for qualitative values which should be independent of quality role type and that quantity has something to say about their instances independently of their corresponding quality, e.g., “large is larger than small” and “green is the complement of red”(Dolce) show it is not appropriate. Quality and quantity must have their own hierarchies to represent their mutual independence. At the same time, their tight relationship must be modeled appropriately.

Now, what is quantity? Quantity is what is denoted by its measurement. We never know the true quantity of anything because measurement is always incomplete. What is correct is that there are two quantities: true quantity and its measurement in which the latter is an approximation of the former. True quantity is unit-independent. It is independent of how long 1m is. We will come back to this issue later.

3.3.2 is-a hierarchy of quantity Quantity has its own hierarchical structure as shown in

Fig. 8. Major features of this quality value hierarchy include separation of categorical and quantity, and introduction of qualitative values. By categorical, I mean genuine categorical quality value such as viviparous/oviparous, colors such as red, blue, green, etc. Note here that categorical value and qualitative

Fig. 8 Quantity

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(quantized) value are intrinsically different. While categories have typicality, qualitative values do not. For example, red as a category has the typical redness at a certain frequency with peripheral redness at higher and lower frequencies. On the other hand, quantized qualitative values do not have such typical thing but still have, like quantity, ordinal relationship between values which categories do not. Quantity is further divided into quantitative quantity and qualitative quantity. The former is divided into attribute-neutral and attribute-specific, and the latter includes “large”, “high”, “big”, etc. Examples of attribute-dependent qualitative quantity include long, heavy, expensive, etc. Quantitative quantity includes ordinary values such as length quantity, weight quantity, etc. Large_small is special in the ontology of quantity. It is introduced to make powerful qualitative values. Examples include high/low, big/small, etc. One of the well-known issues related to these values is how to realize qualitative values that are compliant with “A small elephant is bigger than a big ant” while guaranteeing “big” is larger than “small” in each context. Large_small realizes such qualitative values in a sophisticated way. Details are not discussed here. Those who are interested in it are encouraged to read the ontology. This is one of the most remarkable advantages of YAMATO over existing upper ontologies which cover only higher level types which are nowadays becoming a bit obvious.

3.3.3 Confusion about ontology and data description

Quantity is intrinsically closed to description, since it must be measured to be known by humans and then it must be described to exist as data about the measured entity. Without measuring, we cannot talk about particular quantity. This is an aspect of quantity that is tightly connected to description. However, we have to understand that quantity is ontologically measurement-independent, and hence it is unit-independent, that is, length quantity, for example, can exist as the same quantity independently of how long 1m unit is. What is influenced by the size of the unit is the measurement result which is a description (representation). Quantity is tightly connected to representation in another sense, e.g., a length quantity has multiple ways of representation depending on which unit is used among km, m, cm and mm or inch, etc. In YAMATO, these issues are clearly covered which are not covered by BFO or DOLCE. YAMATO has ontology of data representation as well as ontology of quality

discussed thus far, which is discussed below in 4.4. There are two kinds of unit: one whose size is

standardized like 1 m and the other one that represents a kind of quantity such as length. In YAMATO, the former is called “The unit” and the latter “unit”.

3.4 Quality and its description There must be a clear distinction between reality and its description. That is, <E, A, V>, <E, P> and <E, P, V> are not reality but quality description of reality. Note here, however, that these descriptions are also reality in the sense that they exist as data or description just like books exist. This two-level reality is one of the sources of confusion about quality-related issues. Both must be included in ontology with clear distinction between the two. As far as the author knows, both BFO and DOLCE deal only with the primary reality, that is, they do not deal with quality description. YAMATO would be the first ontology which takes care of both.

In order to deal with description properly, we first need to establish ontology of description/representation. As usual, BFO deals with representation (informational object) only at the highest level. It is called generically-dependent entity and it is not further elaborated what they are. The author has once proposed the ontology of representation(Mizoguchi 2004) which has not been well-disseminated yet. In this paper, we re-visit the topic in more detail with some modification of the old one in Section 4.

3.5 Evaluation and discussion Examples of several quality descriptions are shown in Fig. 9 in which “(XYZ)” shows the example is the way recommended by XYZ ontology. These are presented for demonstrating variety of existing data descriptions and how well YAMATO can cope with them. Note here that <E, A, V>-type description is de facto standard in all the engineering data and that <E, P, V>-type descriptions are often found in clinical domains. These facts strongly suggest that only BFO or DOLCE cannot cover existing quality descriptions by itself. As we have discussed above, all the attributes of an entity are quality roles including degenerated cases, and hence “A” in <E, A, V> represents only quality role type and do not represent generic quality type such as length(1D-extent), weight, mass, etc. Precisely speaking, therefore, the description “(DOLCE) <E, Ai, Vj>” in Fig. 9 should be understood as “DOLCE supports <E, A, V>-type of description” excluding the

1. He is tall. (BFO) <E, P1>2. He is 185cm high. (BFO) < E, P2>3. His height is high/big/large. (DOLCE) < E, A1, V2>4. His height is 185cm. (DOLCE): < E, A1, V1>5. This rose is red. (BFO) < E, P3>6. The color of this rose is red. (DOLCE) < E, A1, V3>7. The color of this rose is xyz Hz. (DOLCE) < E, A1, V1_1>8. The redness of the color of this rose is high. (Galen) < E, P3, V2>9. This rose doesn’t have redness. (Galen) < E, P3, V4>10. Diarrhea of this patient is severe (Galen) < E, P4, V2>11. The length of the pen is short. (DOLCE) < E, A1, V5>12. The conductivity of this material is high. < E, A2, V2>13. The insulativity of this material is high. < E, A3, V2>14. This road has many curves. < E, A4, V6> (This road is curvy)15. Tom visited Kyoto three times. < E, A5, V7> (He is a frequent traveler)

Fig. 9 Examples of quality description.(See appendix for Ai, Pj, Vk)

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meaning of “DOLCE supports Ai”. As shown in Fig. 9, various quality descriptions are supported by YAMATO. Among them, descriptions 14 and 15 need special attention. “many” (curves) and “many times” are qualities not of “curves” nor of “events”, but of the road and Tom, respectively.

We formulated the mutual transformation between the above three kinds of representation. We have conducted two evaluation experiments of our quality ontology as well as the transformation. One has been done using Nanotechnology Index Ontology (NIO) developed by Yamaguchi, et al.(Yamaguchi 2010) and the other using clinical observation descriptions. NIO consists of 2,300 concepts in its is-a hierarchy. These concepts are categorized into 5 categories (Process, Structure, Function, Material, and Application). In clinical observation, we used all the 3465 observations contained in the master file of MEDIS(Medis 2010) which is currently used in the description of clinical observations in Japanese medical practice. In both cases, we confirmed our ontology and the transformation among three kinds of quality descriptions works quite satisfactorily. In addition, Masuya has been demonstrating YAMATO’s role of promoting interoperability for integration of mouse phenotype databases(Masuya 2009) in which ontology of quantity has been exploited as well as the transformation formalism among three kinds of quality description.

YAMATO’s ontology of quality and quantity is more complex than that of BFO and DOLCE. People might consider this is a drawback of YAMATO. But, it is not the case. Although they are simple and seem to be right, BFO and DOLCE deal only with high-level types so that it is not enough to help people capture the reality and cannot support variety of existing data descriptions by itself. YAMATO’s ontology of quality and quantity has been achieved thanks to the power of our role theory. The differentiation between height and length (one-dimensional extent) is beautifully realized by introducing quality role type which shows that it is tightly associated with an entity which necessarily differentiates height from length(1-D extent) which is not quality.

4 Ontology of informational objects Ontology of representation (informational object) is badly needed. Imagine WWW information resources. All of them are representations. It would not be a useful ontology if it does not contain presentation in it. By representation, we here mean “content-bearing thing”. That is, anything which has content as its essentials rather than itself which is playing the role of carrier/bearer of the content. A typical example is a sentence. What exist in WWW, that is, what we can be reached at URLs are not real entities but representations. Similar to WWW, there exist quite a few representations in the real world: novel, poem, painting, music, procedure, symbol, etc. What is the instance of a representation? How are representations different from real-world individuals? These are the questions to answer in this section. To answer them, we need a sophisticated ontology of representation. What are the instances of procedure, music, drama, symbol, calligraphy, painting, poem and novel? Some look easy to answer, but others might look difficult. Concerning novel, there are three kinds of candidates for its instance: a book of the novel,

the sentences of the novel and their meaning (story). Concerning the procedure, a document of the procedure description, the procedure description, its meaning (sequence of steps) and its execution of those steps are the candidates. Similarly, a piece of music also has four candidates: a musical score book, the musical score, the sound people hear and the playing action which produces the sound. As the above examples suggest, the source of the difficulty in answering these questions is that a representation has several deeply-related concepts such as its embodiment, the mode or the form of representation and its content.

4.1 A conceptual model of representation A representation is composed of two parts, form and content shown in Fig. 10(a) like SUMO(Pie 2010)9. A representation is not concrete yet as it is. It becomes a physical individual only when it becomes a representing thing shown in Fig. 10(b). Top-level structure of representation is shown in Fig. 11.

9 Part-of relation here should be understood as constituted-of rather than mereological part-of.

Fig. 11 Top-level structure of representation

(a) Representation

(b) Representing thing

Fig. 10 Slot structures of representation and representing

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This separation is critical. Without this we could not expect a convincing ontology of representation. We need to realize something exists as content independently of its representation. Content is the hidden part of representation and it is a proposition which the author of the representation would like to convey through the representation. Apparently, there can be many ways to code the same content into different forms to produce different representations. The identity of “Representation” is made of both form and content. If their contents are different, then the representations are different. Concerning things of the same content, the identity is determined only by form which is usually what people sense its existence. When the language is written down on a sheet of paper, it becomes a representing thing.

Figs. 12 and 13 show is-a hierarchies of representation form and proposition, respectively. The former is divided into ordinary form and unit-related form. As is seen by the subclasses of ordinary form, typical representation form includes language as a symbol sequence.

Unit-related form is special because it is introduced to cope with quantity as representation discussed in Section 3 and is discussed later intensively. Ordinary form is divided into symbol sequence and image form, and the latter into still image and motion image.

Proposition is what to be represented and is divided into representation-primary and representation-secondary. The latter includes fact, data and thought, etc. By fact, I mean a happening that a human has recognized and is ready for representation to talk about it. The very fact happening in the real world is an instance of event. Representation-primary proposition has two subclasses: designed proposition and product proposition. The former works as specification of the production of something. The latter itself is the product. For example, the content of a piece of music is a specification of the music sound produced by a music player. Content of a procedure is specification of the valid sequence of actions. An execution of the procedure generates a result(product). Novel cannot be specification of anything because it is already a product. Note that as will be discussed later, appreciation of a novel is different from specification which is common to anything.

4.2 Evaluation and discussion It is important to clearly distinguish between a representation and a representing thing. Any representation is not embodied unless it becomes a representing thing. A sentence “This is a book” is a representation in the form of natural language(English) whose content is the meaning of “This is a book” and what you see is its printed realization on a sheet of paper which is a representing thing. Before writing it down, the symbol sequence “This is a pen” is not a physical individual because it does not specify what particular icon of symbols are used to represent each of the symbols. Symbols without icon are semi-abstract individuals as discussed below. Note here that “This is a pen” before writing it down, that is, before becoming a concrete thing is not something in one’s mind but simply a symbol sequence independently of where it exists.

4.2.1 On copying There seem to exist two kinds of “copy” of

representation by symbol: (1) copying the symbol sequence as a symbol level thing and (2) copying the symbol sequence as an image(photo-copying). YAMATO’s representation ontology covers both (1) and (2). Copying of type (1) cannot be done for representation because any sequence of symbols is unique and is

Fig. 13 Is-a hierarchy of proposition

Fig. 12 Is-a hierarchy of representation form.

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independent of what concrete icons of letters are used. That is, there is only one “This is a book” sentence in the world at the representation form level10. In other words, contrary to intuition, what you can type-(1)-copy is only representing thing. In such cases, you can copy it in any hand-written letters or type it in different fonts and sizes. It is obvious that type-(2)-copying can be done only for representing things. In the following, therefore, I use the term “copy” discarding the distinction between types (1) and (2). The copied stuff is what is on the representation medium in both cases. Copying is just a generation of the same representation on a different medium. That is, what you can copy is not representation but representing thing. In fact, a novel, say, Tale of Genji, exists in the form of a book. A copy of a book is physically a 3D thing with a logical structure of chapter, section, etc. and with the content composed of a representation in terms of sentences/images. Tale of Genji exists independently of on what medium it is written.

4.2.2 Identity Identity of a representation/representing-thing is

divided into four kinds: (0) content level, (1) symbol level, (2) icon level and (3) medium level. Obviously, at the content level, two representation/representing-things are identical iff the contents are identical. At the symbol level, the identity comes from the representation form, that is, they are identical iff the representation forms are identical in terms of symbol sequence. At the icon level, they are identical iff the representation forms are identical in terms of icon level. The medium level applies only to representing things, and two representing things are identical iff they are icon-level identical and their media are the same as physical individuals. That is, it follows the common principle of identity of physical entity. Therefore, a hand-written copy of a sentence on a sheet of paper is identical with the original one, at the level (1), iff there is no transcription error. A photocopy of a sentence on a sheet of paper is identical, at the level (2), with the original one iff the photocopying quality is higher than a threshold and they are always identical with each other in terms of symbol level. Concerning medium level identity, there is only unique representing thing, since copying physical entities is impossible in principle.

4.2.3 Some examples It is the time to discuss what are procedure, music, etc. The following lists samples of definitions of some types and individuals: Algorithm representation is-a: Representation p/o"form": Language p/o"content": Algorithm A representation of Quicksort algorithm with C instance-of: Algorithm representation p/o"form": <C language> p/o"content": <Quicksort algorithm> Musical score

10 Do not confuse “This is a pen” as a representation with “This is a pen” as representation form. While the former includes its content and exist in the world as many as its content denoted by it (representation), the latter is just a symbol sequence.

is-a: Representation p/o"form": Musical symbol sequence p/o"content": a piece of music A score of symphony, the 5th

instance-of: Musical score p/o"form": <A sequence of musical symbols> p/o"content": <Symphony, the 5th> A copy of book of musical score of the 5th

instance-of: Representing thing p/o"representation": <A score of symphony, the 5th> p/o"medium": <Pieces of paper>

Sentence is-a: representation p/o"form": natural language

p/o: sequence of alphabets p/o"content": proposition(the meaning) <This is a book> as a sentence

instance-of: Sentence p/o “form”: <This is a book> as a symbol sequence p/o “content”: <the meaning>

<This is a book> as a symbol sequence instance-of: symbol sequence which is-a

representation form p/o: ”T”,”h”,”i”,”s”,” “,”i”,”s”,” “,”a”,…..

<This is a book> as a speech instance-of: Representing thing p/o “representation”: <This is a book> as a sentence p/o “medium”: <a sound>

<This is a book> as a written sentence instance-of: representing thing p/o “representation”: <This is a book> as a sentence p/o “medium”: <a piece of paper>

The above models declare that an instance of an algorithm is composed of an instance of language description called form and an instance of proposition which is a subclass of designed proposition called content. It can explain various representations, as instances, of quick sort algorithm by changing the form part which can take not only the computer languages C, Lisp, Java, etc. but also the real code in such a language keeping the same content, Quicksort algorithm. Note here that an instance of an algorithm is not a sequence of actions performed according to the algorithm description but a specification of valid action sequences. That is, an instance of an algorithm is a specification of its execution. A specification can virtually exist not as being an embodiment(representing thing), but as the content of representation. In general, all the designed propositions are specification of their succeeding realization actions.

The next problem might be what is the sound (symphony the 5th) people hear? It is an instance of musical sound and is a realization of the symphony the 5th, not an instance of a piece of music which should be constructed in the hearer’s mind by interpreting the sequence of musical sound and coincide hopefully with the specification of the piece of music. The playing action is an instance of playing action and at the same time a realization action of the musical sound. Furthermore, the relation between the musical sound and symphony the 5th is realization-of relation. Fig. 14 shows an is-a hierarchy of representation.

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4.3 Quality representation As was discussed in Section 3, quality representation

must be dealt with explicitly with careful attention on distinction between reality and description of reality. YAMATO introduces tupple, triple and unit-related form as representation form(Fig. 12), E_A_V, E_P_V, and E_P as representation of quality, and quantity representation (Fig. 13) for dealing with m, cm, mm, etc. Fig. 15 shows definitions of measure, cm length form and cm quantity representation. Measure somehow transforms the real quantity to its approximation as a representation, that is, we understand the measurement produces a representation. In the ontology in Fig. 15, the measurement result is referred to as quality measurement which is a role holder and must be an approximation of the real quantity which should be unit-independent. Quality measurement(RH) is referred to in the class constraint of the content slot of cm quantity representation to represent the measured quantity in the form of cm. The length representation is referred to as length in cm role holder in the form slot of cm quantity representation. Cm length form is defined using unit of length and value slot which stores a number as a value referring to 1m unit length as the standard length. It also defines cm as a role holder which is a new finding on how to define cm, mm, km, etc. In summary, quantity is made

accessible as a proposition as a result of measuring. Then, it is representing in, say, cm quantity representation in which length in cm of the quantity is obtained. Thus, a quantity is made an accessible thing as a representation form in a representation rather than a proposition keeping the measured quantity in its corresponding proposition.

On the basis of the preparation, a unique type named equivalence is introduced to explicitly show the correspondence between the three ways of quality descriptions. Although this topic is interesting to discuss, details are omitted in this paper.

5 Objects, Processes and Events Although this topic is the most philosophical and hence the most important, we here present only the summary of the discussion as follows because it is in-depth discussed in (Galton 2009):

(Excerpt from (Galton 2009)) Any change must be a change of something. This is already an argument against a ‘pure process’ view of reality, since we cannot conceive of processes without their material support. One might ask: what is a person over and above the sum of its internal processes? But what makes this sum worthy of consideration at all is that they constitute some kind of unity; the unity comes from the fact that there are other processes, its external processes, which it enacts. Thus these questions make the mistake of focusing only on the internal processes of a person, whereas the external processes play an essential role in determining the identity of the object.

Fig. 15 Measurement and length form.

Fig. 14 Hierarchy of representation.

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Hence, rather than trying to characterize an object in terms of its internal processes (e.g., by identifying the object as the sum of those processes), we would rather say that an object is a unity which is what enacts its external processes. We could indeed say that the object is the interface between its internal and external processes: it is a point of stability in the world in virtue of which certain processes are characterized as internal and others as external. The issue of external vs. internal processes summarizes as “The water falls, but the waterfall doesn’t fall”. That is, what a waterfall is doing is not the water falling but migration upstream as it carves its way into the rock.

Similarly, what a river is doing is not the water flow but changing the shape of its course of the flow. This is why we can consider a river is an object which has water flow as its inner process.

Another important topic is what can change. It is also summarized as follows(see (Galton 2009) in detail): An event cannot change. This is not because it is already a change, but because it exists with unity in the temporal space, that is, it must be always viewed as a whole. Events are made of processes. Processes are dissective and hence they have no unity. It has no whole, and hence it has no (temporal) part. Processes are essentially on-going stuff and hence they can change. YAMATO is based on these findings and has sophisticated upper categories of events and processes.

Parts of an occurrent in YAMATO need discussion. There are two kinds of parts of occurents: temporal parts and causal parts. While the former correspond to mereological parts of continuant, the latter to functional parts. Considering that occurrents are things in the temporal space, the idea of mereological parts is straightforward, that is, interval-based segmentation for identifying parts makes sense. However, any process and event has its causal parts. Imagine, John sneezes while he is walking. The sneezing is nothing to do with his walking and hence it is not a causal part of his walking. On the other hand, the motion of his legs is essential to his walking. The alternate motions of his left and right legs are causal parts of his walking. The bending motions of his both legs are causal parts of the leg motion. Any causal part is temporal parts, but, not vice versa.

YAMATO is said to be based on 3D view because it clearly distinguishes between continuant and occurrent, at the same time, however, it is said to be based on 4D because it accepts what exist in the world are occurrents rather than continuants. It is based on a solid understanding on what can change and what is an object at all. I could say YAMATO is 3.5D by which, I mean it is based on the idea of neither “objects prior to processes” nor “processes prior to objects, but “both are mutually dependent”.

Events are composed of sub events and all those events are constituted by processes as material. Actions whose operand is anything other than actions are divided into explicit action and state action. The former represents actions which imply how to do it, while the latter actions which mainly imply what state change(what to do) occurs keeping how to do it implicit. The implications of this classification of actions are rich and new. While walk belongs to the former, move to the latter. YAMATO distinguishes between arrive as an action and arrival as an event. As described above, an action is essentially

on-going stuff, while an event is a unitary whole. An action exists in an open interval without either end of the time interval, while an event exists in a closed interval. So, an action arrive does not include the very end point.

The separation of what to do and how to do is the very philosophy of our functional ontology (Kitamura 2006, 2010) which provides us with an innovative view of actions.

6 Roles, functions and relations Roles are not adequately visible in YAMATO, since it is already reflected/embedded in Hozo tool. While ordinary types such as human, table, etc. are defined independently of each other, roles are defined within a context which they necessarily depends on in our role theory (Mizoguchi 2007). In fact, roles are used in defining all the types in YAMATO. These are the reasons why YAMATO does not have to incorporate roles in it. When one uses Hozo with YAMATO, he/she can enjoy maximally the benefits offered by both.

Kitamura and I have been intensively involved in building functional ontology for years(Kitamura 2006)(Mizoguchi 2009b). Although we have already developed a convincing functional ontology which is compliant with YAMATO, it is not incorporated into YAMATO because it is too professional for general readers.

Relations are not incorporated in YAMATO neither because Hozo deals with relations and the wholeness concepts (ordinary types) in different worlds. Similarly to Roles, YAMATO implemented in Hozo exploits built-in and user-defined relations. Hozo has three built-in relations: is-a, part-of and attribute-of which are exploited to define types in YAMATO. These are used to introduce fundamental definitions of types, and user-defined relations are used to impose semantic constraints among parts and attributes of a type.

7 Concluding remarks YAMATO has been implemented in Hozo and is available at http://www.ei.sanken.osaka-u.ac.jp/hozo/onto_library/ upperOnto.htm with a tool-independent browser. Its OWL version will be available soon. It has been axiomatized in the EuJoint project(Borgo 2010). YAMATO was first built in 1999. Since then, it has been refined and revised several times. The current version has been extensively used in several projects such as development of medical ontology(Kou 2008)(Mizoguchi 2009a), ontology of learning and instructional theories which is the first ontology in the community (OMNIBUS), mapping ontology between PATO and YAMATO (Masuya 2009), ontology of genomics (GXO (Masuya 2009)), modeling of mobile users’ behavior(Sasajima 2008), functional ontology(Kitamura 2006), etc.

As is shown in 3.5 on evaluation, ontology of quality representation has been well evaluated and its utility has been demonstrated. Our role theory has been used more than ten years with Hozo tool, which suggests it has been already well-established. Ontology of representation is being used in Genomic ontology, GXO (GXO). Although the object/process/event ontology is rather new, it is carefully designed to be compatible with our functional ontology. The key point is the structure of action whose

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taxonomic structure is designed based on device ontology so that it is clearly differentiated between what is performed and how it is performed. In summary, YAMATO, an upper ontology which has appeared at last after DOLCE, BFO, GFO, SUMO and CYC, would be a powerful ontology in the three respects discussed in this paper. Its full power can be enjoyed when it is used with Hozo.

Acknowledgement The author is grateful to my colleagues Yoshinobu Kitamura, Kouji Kozaki, Munehiko Sasajima and Yusuke Hayashi for their valuable comments. Special thanks go to Stefano Borgo for his comments during his work on axiomatization of YAMATO.

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Yoshinobu Kitamura, Yusuke Koji and Riichiro Mizoguchi (2006): An Ontological Model of Device Function: Industrial Deployment and Lessons Learned, Journal of Applied Ontology (Special issue on “Formal Ontology Meets Industry”), Vol. 1, No. 3-4, pp. 237-262.

Yoshinobu,K and Mizoguchi, R. (2010): Characterizing Functions based on Ontological Models from an Engineering Point of View, Proc. of the Sixth International Conference on Formal Ontology in Information Systems (FOIS 2010), Toronto, Canada, May 11-14, pp. 301-314, IOS Press.

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Masuya, M. and Mizoguchi, R. (2009): Toward fully integration of mouse phenotype information, The 2nd Interdisciplinary Ontology Conference, pp. 35-44, Tokyo, Japan.

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Mizoguchi, R. Bourdeau, J, and Hayashi, Y. (2010) http://edont.qee.jp/omnibus/doku.php

Yamaguchi, Y. et al. (2010) http://mandala.t.u-tokyo. ac.jp/english/index. html and Development of Contents Management System Based on Light-Weight Ontology, K. Kozaki, Y. Kitamura and R. Mizoguchi: Proc. of the 2007 IAENG International Conference on Internet Computing and Web Services, Hong Kong, 21-23 March, pp.987-992, 2007. http://www.ei.sanken. osaka-u.ac.jp/pub/kozaki/IMECS2007_koza_cr.pdf

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Smith, B. et al. (2010) http://www.ifomis.org/bfo

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Appendix : Details of quality and quantity hierarchy shown Fig. 9.

property– qualitative property

• intrinsically qualitative(P3)– attribute-inclusive(P1)

• extrinsically qualitative– attribute-inclusive

» being diarrhea(P4)– quantitative property(P2)

generic quality (attribute)– intrinsic generic quality

• basic generic quality– non-meta generic quality(A1)– meta-generic quality

» counting generic quality+ number of objects(A4)+ number of events(A5)

• I_O relational– continuous

» forward/(A2)» backward(A3)

– Accidental generic quality quality value

– categorical(V3)– quantity

• quantitative quantity– singleton

» attribute-specific+ ordinary quantity

- length quantity(V1)- frequency quantity(V1_1)

» attribute-neutral• qualitative quantity

– attribute-inependent» binary_value

+ non-meta value- quantity quality value(V2)

+ meta attribute value- counting_value(V6)- times quality value(V7)

– attribute-dependent» length quality value(V5)

15

16

A Visual Analytics Approach to Augmenting Formal Concepts withRelational Background Knowledge in a Biological Domain

Elma Akand1 Michael Bain1 Mark Temple2

1 School of Computer Science and Engineering,University of New South Wales,

Sydney, Australia 2052

Email: {akande,mike}@cse.unsw.edu.au

2 School of Biomedical and Health Sciences,University of Western Sydney,

Campbelltown Campus,Locked Bag 1797,

Penrith South, Australia 1797

Email: M.Temple@uws.edu.au

Abstract

Formal Concept Analysis provides a rigorous frame-work in this paper to combine visualization and ma-chine learning for a complex application in systemsbiology. We develop a concept lattice constructionalgorithm based on techniques from frequent itemsetmining and adapt local browsing of concept latticesas the visualization approach. A web-based interfaceenables the user to navigate the concept lattice eas-ily to inspect formal concepts for further processing.This includes integration of concepts with externaldata sources, including relational data representingbiological networks, and machine learning using In-ductive Logic Programming. Initial results are pre-sented on a significant real-world data set showingthat the approach can generate biologically promis-ing hypotheses for further analysis.

Keywords: Visual Analytics, Formal Concept Analy-sis, Closed Itemset Mining, Systems Biology, Induc-tive Logic Programming.

1 Introduction

Visual analytics (Keim, Mansmann, Schneidewind,Thomas & Ziegler 2008) combines automated meth-ods of machine learning and knowledge discoverywith visualization techniques to enable human do-main experts to apply their background knowledgeand decision-making skills in the exploration of de-manding data analysis problems. Although data vi-sualization and model visualization are usually con-sidered separately, in this paper we use Formal Con-cept Analysis (FCA) (Ganter & Wille 1999), a dataanalysis framework appropriate for discrete domains,that combines both data objects and their descriptiveattributes in a unified concept lattice, integrated witha browser interface and machine learning tool.

Our approach is motivated by applications inmolecular systems biology (Ideker, Galitski & Hood2001), which is developing rapidly in the post-genomeera (Kanehisa 2000). This will provide a novelmethod to link observable cell-level characteristics

Copyright c©2010, Australian Computer Society, Inc. This pa-per appeared at the Sixth Australasian Ontology Workshop(AOW 2010), Adelaide, Australia. Conferences in Researchand Practice in Information Technology (CRPIT), Vol. 122,Thomas Meyer and Mehmet A. Orgun and Kerry Taylor, Ed.Reproduction for academic, not-for profit purposes permittedprovided this text is included.

(phenotypes) generated by modest research labora-tories with large scale post-genomics data sets of-ten generated through cutting-edge high throughputtechnologies. This will enable biologists to evaluatethe results of a genome-wide phenotypic study (suchas a screen of the library of single gene knock-out mu-tations to a treatment to determine which genes arenecessary for survival – the yeast deletion library) incontext with large scale data sets encompassing hun-dreds of thousands of protein-protein or genetic inter-actions.

Our long-term goal is to enrich the process of dataanalysis and mining with domain knowledge fromusers, to which this paper contributes as follows.

First, although the space of formal concepts orclosed itemsets is reduced relative to that of all item-sets (Pasquier, Bastide, Taouil & Lakhal 1999), thisstill results in large numbers of formal concepts ontypical real-world data sets. In this paper we developan improved algorithm for closed itemset mining thatgenerates a browsable concept lattice designed forsystems biology applications. Additional criteria toselect or rank concepts from the space can be use-ful (Akand, Bain & Temple 2010), and in our exper-iments we explore statistically motivated criteria toevaluate potentially interesting concepts.

Second, integration of multiple sources of knowl-edge that can be used for the intents of formal con-cepts is often useful. However this can cause prob-lems, either in expanding the attribute set, whichleads to increased computation time in lattice con-struction, or extending the expressiveness of the rep-resentation, which leads to greater complexity inthe FCA framework and algorithms (Carpineto &Romano 1996). An alternative method we investi-gate is integration of knowledge after construction ofthe lattice using an initial set of attributes.

Third, for human domain experts visualization ofthe concept lattice enables an overview of the struc-ture of the domain and assists in data analysis andmining. Since the concept lattice is usually too largeto be viewed in its entirety only localized viewing andnavigation of the space is possible (Priss 2006), andwe take a similar approach.

Fourth, following the visual analytics ap-proach we add a machine learning capability.MINER (Kadupitige, Leung, Sellmeier, Sivieng,Catchpoole, Bain & Gaeta 2009) is an interactivemethod of guiding data mining for genomics data, butis restricted to propositional learning. In this paperwe apply Inductive Logic Programming to learn defi-nitions of selected concepts in the lattice; this allows

17

the integration of relational background knowledge ina data-driven post-processing phase of concept anal-ysis.

Finally, viewing the construction of formal con-cepts and their lattice as one stage of an analyticsprocess which we describe below for an application toa systems biology domain suggests a possible role forontology construction using methods from our previ-ous work (Bain 2003).

The remainder of the paper is structured as fol-lows. Section 2 reviews closed itemset mining and itssuitability as a model class for visual analytics anddescribes the method we use to construct a lattice ofclosed itemsets. In Section 3 we outline our approachto visualization of the space of closed itemsets basedon ideas from Formal Concept Analysis for browsinga lattice. Section 4 discusses the systems biology taskinvestigated in this paper, with conclusions and fur-ther work in Section 5.

2 Closed itemset mining

A standard problem in data mining is finding allitemsets and their associations, usually expressed inthe form of association rules, given certain parame-ters (Agrawal, Mannila, Srikant, Toivonen, Verkamoet al. 1996). However, it is well-known that this canresult in a very large number of itemsets. In prac-tice this can typically be reduced by using a non-redundant representation of the set of itemsets such asthat provided by the set of closed itemsets (Pasquieret al. 1999). This framework is closely related to For-mal Concept Analysis (FCA) (Ganter & Wille 1999),which also provides an approach to visualization ofthe resulting lattices of itemsets, and hence we willuse both FCA and itemset mining notation and ter-minology interchangeably throughout this paper.

2.1 Formal Concept Analysis

We apply Formal Concept Analysis, a well-known andwidely-used method to explore concepts and their hi-erarchical relations, given a set of observations or-ganized in a formal context. Here we formalise thecontext in the background of a set of extra-cellularmultiple response phenotypes in yeast.

In this context let 〈D,O,R〉, the set of descriptorsD represents a set of stresses, the set of objects Orepresents a set of genes, and R is a binary relationdenoting the response of genes to stresses. Thus eachformal concept is an ordered pair of set 〈X,Y 〉, whereY ⊆ O and X ⊆ D. Therefore, X ′ = Y and Y ′ = X,whereX ′ = {y ∈ O|∀x ∈ X,xRy} andY ′ = {x ∈ D|∀y ∈ Y, xRy}.

Following (Ganter & Wille 1999), given two con-cepts C1 = 〈X1, Y1〉 and C2 = 〈X2, Y2〉, we have theorder C1 ≤ C2 ↔ X1 ⊇ X2. The dual nature ofthe Galois connection means we have the equivalentrelationship C1 ≤ C2 ↔ Y1 ⊆ Y2.

In terms of our stress response example, this canbe explained simply as: if we increase the amountof stress in a concept, the combined response in ge-nomic terms will decrease, i.e., the concept becomesmore specific. Decreasing the amount of stress hasthe opposite effect, i.e., generalizing the concept.

For example, the concept 〈 {H2O2 Thorpe,CHP Thorpe, GHS homeostasis, Diamide Thorpe}{EOS1, HFI1, PAF1, URE2} 〉 shows a particularset of genes sharing these common stresses which isexclusive to them. Any additional stress, such as Sor-bate, results in removing the genes {EOS1, URE2}from the concept to form the subclass concept 〈{H2O2 Thorpe, CHP Thorpe, GHS homeostasis, Di-amide Thorpe, Sorbate}, {HFI1, PAF1} 〉. Like-

wise, removing a stress such as CHP Thorpe resultsin an extra gene FAB1 added to the existing set ofgenes to form the super concept 〈 { H2O2 Thorpe,GHS homeostasis, Diamide Thorpe}, { EOS1, HFI1,PAF1, URE2, FAB1} 〉.

Thus we have a subsumption hierarchy followingthe order ≤ defined above which gives rise to a com-plete lattice. Concepts close to the top of the lat-tice depict the picture that more genes combinedlyrespond to fewer stresses, whereas concepts close tothe bottom have only a few genes responding to alarger set of stresses. This formalisation provides uswith the basis for a method to extract the concepts,to visualize them and relate them to other sources ofdata, such as annotation of their gene functions usingthe Gene Ontology (Ashburner et al. (2000)) data ontheir activity such as microarray measurements andprotein-protein interactions.

2.2 A concept lattice algorithm to supportvisual analytics

Many different algorithms have been proposed to con-struct concept lattices: see (Kuznetsov & Obiedkov2001) for a review. All these algorithms are subject tothe bottleneck of generating all of the concepts in thelattice. It is a well known problem that the computa-tional complexity of generating all concepts in the lat-tice becomes critical as the number of concepts expo-nentially increases with the size of the input context.The complexity of mining closed itemsets (formal con-cepts) for a given level of support has been shown tobe #P-complete (Yang 2004), i.e., intractable in theworst-case.

Therefore, work on formal concept analysis andclosed-itemset mining has tended to focus either onmaking approaches more efficient or enabling concep-tual analysis. On one hand there are algorithms tospeed up closed itemset mining for conceptual knowl-edge discovery or data mining such as CHARM (Zaki& Hsiao 2005). On the other hand, implementa-tions of formal concept analysis tend to have a fo-cus on elegant visualizations of entire concept lat-tices, but restricted to smaller datasets, such asTOSCANA (Eklund, Groh, Stumme & Wille 2000)for conceptual information systems.

However, in systems biology applications the prob-lem is that while typically visualization is a require-ment, the data sets are quite large and heterogeneous,from multiple sources. To address this problem wehave developed a system called BioLattice which is afull-scale implementation of a concept lattice buildingalgorithm that also enables visualization. We havecarefully selected a lattice building algorithm as thecomplexity is biased by the choice of input context.A variant of CHARM (Zaki & Hsiao 2005) is im-plemented to take advantage of its vertical data for-mat representation and its computational efficiencybased on: (a) search performed over an intent-extenttree search space; (b) pruning based on both non-frequent itemsets (as in association rule mining) andnon-closed itemsets.

2.3 Definitions and techniques

Most of the data mining techniques based on Apri-ori (Agrawal et al. 1996) or FP growth (Han, Pei,Yin & Mao 2004) adopt the horizontal data for-mat where each row contains a list of items indexedby an associated transaction index. Alternatively,the vertical data format has set of transaction in-dexes for each single item. Several methods suchas CHARM (Zaki & Hsiao 2005) have demonstratedthe merits of vertical format in outperforming thehorizontal format. The large number of I/O over-

18

{F}{g7}

{F,D}{g7}

{F,D,C}{g7}

{F,D,C,A}{g7}

{I}{g4}

{I,H}{g4}

{I,H,G}{g4}

{I,H,G,C}{g4}

{I,H,G,C,A}{g4}

{B}{g5,g6}

{H}{g2,g3g4}

{E,D}{g5,g6,g8}

{C}{g6,g8}

{E,D,A}{g5,g6,g8}

{E,D,A,B}{g5,g6}

{C}{g6}

{E,D,A,B,C}{g6}

{E}{g5,g6,g8}

{H,G,A}{g2,g3g4}

{H,G}{g2,g3g4}

{B}{g2,g3} {C}{g3,g4}

{H,G,A,B}{g2,g3}

{C}{g3}

{H,G,A,B,C}{g3}

{E,D,A,C}{g6,g8}

{H,G,A,C}{g3,g4}

{D}{g5,g6,g7,g8}

{D,A}{g5,g6,g7,g8}

{B}{g5,g6} {C}{g6,g7,g8}

{D,A,B}{g5,g6}

{C}{g6}

{D,A,C}{g6,g7,g8}

{G}{g1,g2,g3,g4}

{G,A}{g1,g2,g3,g4}

{C}{g3,g4} {B}{g1,g2,g3}

{G,A,B}{g1,g2,g3}{G,A,C}{g3,g4}

{B}{g1,g2,g3,g5,g6}

{B,A}{g1,g2,g3,g5,g6}

{C}{g3,g6}

{B,A,C}{g3,g6}

{C}{g3,g4,g6,g7,g8}

{C,A}{g3,g4,g6,g7,g8}

{A}{g1,g2,g3,g4,g5,g6,g7,g8}

{B}{g3}

Branch processing Search level 2: Prefix {E,D,A}Brach21:{B}{g5,g6}Branch22:{C}{g6,g8}

1. Branch 21 becomes {E,D,A,B}{g5,g6}2. Combine branch22 creates branch31 {C}{g6} under branch213.check closure and add {E,D,A,B}{g5,g6} to lattice

search level 3: Prefix {E,D,A,B}Branch31:{C}{g6}

4. Branch 31 becomes {E,D,A,B,C}{g5,g6}5.check closure for branch31 and add {E,D,A,B,C}{g5,g6} to lattice6.Backtack to search level 2 to process branch22; which becomes {E,D,A,C}{g6,g8}; check closure and finally add to the lattice

root{}

Figure 1: BioLattice intent-extent search tree. Candidate concepts are shown as intent, extent pairs. SeeSection 2.5 for details.

head operations for candidate generation and count-ing support at each single step, complex internal datastructures with hash/search tree are significant draw-backs while mining dense dataset with horizontal for-mat. However, mining based on intersection of read-ily available transactions of itemsets where support isequivalent to the length of the transaction indexes isa relatively easy task in vertical format. Moreover,this approach enhances pruning of irrelevant transac-tion indexes at each intersection operation and offersscope for compression.

Fast computation of frequent closed concept min-ing is achieved by dividing the search space based onindividual prefix based equivalence classes. As in thefigure 1, each node in the tree has intent-extent pair〈Pi〉〈Pt〉, defining a prefix based equivalence class Pi

over all of its children {C1, C2, ...Cn}.For example, At the root, each of the frequent in-

tents {F, I, E,H,D,G,B,C,A} is a possible exten-sion for equivalence class. Starting with the leftmost child with class [F ], all the right siblings thatform frequent subsets {FD,FC, FA} will also sharesame prefix F . Therefore, a class represents set ofcandidate intents that the prefix can be extendedwith to form new specialized frequent concept. Insuch framework, mining frequent concepts is straight-forward. As we see above, given a node or prefixclass, [P ] ={C1, C2, ...Cn}, a new frequent class [PCi ]={Cj} can be mined by intersecting PCi〈extent〉 withall PCj〈extent〉 where j > i in order and itemset{PCiCj} is frequent.

2.4 Properties used for search-space pruning

Pruning is carried out based on four properties de-scribed in (Zaki & Hsiao 2005). Let there be twocandidate concepts derived from the context, Ci andCj . The properties are described as follows.

1. if Ci〈extent〉 = Cj〈extent〉, then replaceCi〈intent〉 with the more specialized intentCi〈intent〉 ∪ Cj〈intent〉 and remove candidateconcept Cj from the context;

2. if Ci〈extent〉⊂Cj〈extent〉, then replace Ci〈intent〉with the more specialized intent Ci〈intent〉 ∪Cj〈intent〉;

3. if Ci〈extent〉 ⊃ Cj〈extent〉, then add a special-ized branch Cb under Ci with intent Cj〈intent〉and extent Ci〈extent〉 ∩Cj〈extent〉. Also removecandidate concept Cj from the context;

4. if Ci〈extent〉 6⊂ Cj〈extent〉 and Ci〈extent〉 6⊃Cj〈extent〉 and Ci〈extent〉∩Cj〈extent〉 6= ∅, thenadd a specialized branch Cb under Ci with intentCj〈intent〉 and extent Ci〈extent〉 ∩ Cj〈extent〉.

2.5 Algorithm Design

This section presents an overview of the algorithm tosearch for closed frequent concepts over the intent-extent search space and organize them in a conceptlattice built incrementally at the same time 2 . Thetop-level of the method is in Algorithm 1.

Algorithm 1 BioLattice(data G, minSup)1: Generate frequent 1-intent candidates and sort them based

on weight function2: Initialize root Lr =φ, IntentCid IC, prefix p = φ, latticeL

3: BioLattice Extend(G, IC, minSup, L, p, Lr)4: return L // Formal concept lattice

In general, the search space of formal concepts orclosed itemsets is reduced by eliminating candidateswhich have less than minimum support specified by

19

Formal context

Divide intent-extent search

space based on frequent n intents (1-candidate itemset)

Preprocess to vertical format , ordered by increasing weight

Find frequent concepts

local to each prefix

equivalence class

Compare closure

globally to prune non-

closed concepts

Add newly found closed

concept to lattice and

update hierarchy

Formal concept lattice

Recursively process branches

Figure 2: Steps to build formal concept lattice

the user, in common with other itemset mining meth-ods. As a pre-processing step a weight function iscomputed for candidate 1-itemset concepts as in (Zaki& Hsiao 2005). Once frequent 1-itemset candidatesare generated, they are sorted based on this weightfunction, which is defined for an item x as the sumof the support of all frequent 2-itemsets containingx. This sorted data becomes the input set G. Theweights for the example in Figure 1 are shown in Fig-ure 3 – note that the weights determine the left-to-right sibling ordering in the search tree of that figure.

descriptor objects Weight

F g7 3

I g4 4

E g5, g6, g8 10

H g2, g3, g4 11

D g5, g6, g7,g8 13

G g1, g2, g3,g4 13

B g1, g2, g3,g5,g6 16

C g3, g4, g6,g7,g8 18

A g1, g2, g3, g4,g5, g6,g7,g8

26

Figure 3: Weight function values for frequent 1-itemsets Figure 1.

A look-up table “IC” mapping intents to their oc-curences in closed concepts that contain them recordsall the frequent intents and thereafter is used for sub-sumption checks. An example of such a table is shownat top left of Figure 4. The concept lattice is stored ina table called “L” containing information on all con-cepts and their hierarchical relations in the lattice.

Whenever a frequent concept is generated, i.e., onewith support above the user-supplied parameter min-Sup, IC & L are accessed to check subsumption and,if found closed, a unique concept index is generated.Based on the subsumption information, a closed con-cept is added into the lattice while maintaining thegeneral to specific order.

Algorithm 2 (BioLattice Extend) generates closedconcepts for each of the equivalence classes, where anequivalence class of intents is those sharing a commonprefix set of items. The resulting search tree for anyequivalence class can be seen as a locally generatedgeneral-to-specific ordered set of concepts, where thetop concept is the most general concept with intentcontaining the prefix shared by all of its specializedsub-concepts.

Algorithm 2 starts with candidate c with the low-est weight and combines it with the next element tocheck that their frequency of occurrence satisfies therequired minimum support. For example, consider-ing {F, I, E, H, D, G, B, C, A} as a set of initialequivalence classes, from Figure 3 F has the lowest

Algorithm 2 BioLattice Extend(G, IntentCid IC,minSup, lattice L, prefix p, root Lr)1: for all xi in G do2: c < intent >= {p} ∪ xi < intent >3: c < extent >= xi < extent >4: branch = φ and closure = φ5: for all xj in G do6: concept < intent >= xj < intent >7: concept < extent >= xi < extent > ∩ xj <

extent >8: if support(concept) ≥ minSup then9: DoSpecialization(concept, xi, xj , branch, c, G)10: end if11: end for12: ComputeClosure(c, IC)13: Ln = AddConceptToLattice(c, L, IC, Lr,closure)14: if Ln 6= Lr then15: sort branch in order of increasing support16: BioLattice Extend(branch, IC, minSup, L, c, Ln )17: end if18: delete c19: end for

weight in the order. F is chosen to start with andwhen combined with {I, E, H, G, B} results in infre-quent candidates, and is thereby pruned. Candidateswith the same or higher support are processed for acheck of the four properties (line 9) by the DoSpe-cialization subroutine defined in Algorithm 3. Twotypes of specialization are possible. Properties 1 & 2indicate specialization by replacing a node by addingextra intents, whereas properties 3 & 4 specialize bycreating branches with reduced extents. With ele-ment {D},{g5,g6,g7,g8}, property 2 is satisfied and{F},{g7} is replaced by {F, D}{g7}, as shown in Fig-ure 1.

Algorithm 3 DoSpecialization(concept N , xi, xj ,branch, p, G)1: if xi < extent >= xj < extent > then2: delete xj from G3: p < intent >= p < intent > ∪ xj < intent >4: else if xi < extent >⊂ xj < extent > then5: p < intent >= p < intent > ∪ xj < intent >6: else if xi < extent >⊃ xj < extent > then7: delete xj from G8: add N to branch9: else if xi < extent > 6= xj < extent > then10: add N to branch11: end if

An example of creating and processing branch canbe seen in the highlighted circle of Figure 1, where thetop node has {E, D},{g5, g6, g8} and the next elementto combine has {B},{g1, g2, g3, g5, g6}. Accordingto property 4, a branch {B},{g5, g6} with reducedextent by intersection is added. Note that, unlikeCHARM, a branch at this point does not have intent{E, D, B}. Furthermore, processing with the nextelement {C},{g3, g4, g6, g7, g8} adds another branch{C},{g6, g8}. Finally, the last element {A},{g1, g2,

20

g3, g4, g5, g6, g7, g8} satisfies property 2, and thechange is recorded only at the top node, replacing{E, D},{g5, g6, g8} by {E, D, A},{g5, g6, g8}. LikeCHARM, our algorithm does not visit branches andreorder and update details every time property 1 or2 is satisfied.

After subsumption checks and lattice updates arecarried out for {E, D, A},{g5, g6, g8}, BioLat-tice Extend is recursively called for next search levelin depth first manner. From the available informa-tion in the prefix {E, D, A} at line 2 of Algorithm 2,branch {B},{g2, g3} forms the full concept {E, D, A,B},{g5, g6}. Combining with the only right sibling{C},{g6, g8}, satisfies property 4 and forms branch{C},{g6}. Before search is extended another level,closure of the concept {E, D, A, B},{g5, g6} is exam-ined and added to the lattice. While search is contin-ued with the prefix {E, D, A, B},{g5, g6}, the onlybranch {C},{g6} forms concept {E, D, A, B, C}{g5,g6} and added in the lattice. Finally, algorithm back-tracks to the root with the prefix {E, D, A}{g5, g6,g8} to process remaining branch {C},{g6, g8} whichthereafter, forms {E, D, A, C}{g6, g8} and is placedin the lattice.

To promote occurrences of property 1 & 2,branches are sorted in increasing order of support.This ordering is done at line 15 of BioLattice Extendjust before a branch is processed recursively. Thisstep reduces the number of levels to be searched withthe possibility of creating fewer branches.

Algorithm 2 calls two subroutines (at lines 12 and13), ComputeClosure (Algorithm 4) and AddCon-ceptToLattice (Algorithm 5), to do the tasks of prun-ing non-closed concepts and building the concept lat-tice. The idea is that a list of more specific conceptsare generated and their support is examined. If anyhas equal or greater support than the candidate, it isnot closed and, therefore, pruned.

Algorithm 4 ComputeClosure(candidateset P,IntentCid IC)1: for all pi in P do2: closures =

⋂ICpi

3: end for4: return closures

ComputeClosure generates a list of all possiblemore specific concepts from the IntentCid table.Based on the intersection of their concept indices andthe corresponding lattice entries, their support can becomputed. For example, from Figure 1 the concept{D, A, B},{g5, g6} (line 2, Algorithm 4) generates:

{C5, C6} = {C1, C3, C4, C5, C6, C11}∩ {C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11}∩ {C5, C6, C9, C10}

In the lattice table L the list of more specificconcepts, C5 = {E,D,A,C,B}, {g6} and C6 ={E,D,A,B}, {g5, g6}, the above concept is clearlysubsumed by C6, but not C5, and is pruned as a non-closed concept. Line 14 of Algorithm 2) enforces thatall of its children listed in the branch will also bepruned as they will generate further non-closed con-cepts.

A unique concept index is generated for each ofthe closed concepts and is recorded in the IntentCidtable by Algorithm 5, AddConceptToLattice (line 6).The final step to add a concept in the lattice requirescorrectly identifying all of its immediately more gen-eral and more specific concepts. The root variable Lrkeeps track of immediately more general concepts andis added as a parent of the newly found closed concept(at line 10-14 of Algorithm 5). Through the previous

Algorithm 5 AddConceptToLattice(candidate c,L,IntentCid IC, Lr, closureS)1: for all si in S do2: if supp(si) ≥ supp(c) then3: return Lr // if Subsumed return current lattice node4: end if5: end for6: key ← newid // generate unique id7: for all intent d in c do8: IC < key > .add d // Insert into IntentCid9: end for10: L< key >< intent >= c < intent > //add concept to

the lattice11: L< key >< extent >= c < extent >12: L < key >< parent >=Lr //add root node as parent13: L< Lr >< child >.add (Lr)//add new concept as child14: Lr=key //update root Node15: S ← sort descending order based on support16: for all si in S do17: for all sj in S do18: if sj < extent > ⊂ si < extent > then19: S.delete (sj) // Remove lower transitive closure20: end if21: end for22: L< Lr >< child >.add (si) //add more specific con-

cept as child23: L< si >< parent >.add (Lr) //update parents24: P = parents(si)25: for all p in P do26: if Lr< extent > ⊂ p < extent > then27: L< p >< child >.delete (si) //Remove upper

transitive closure28: L< si >< parent >.delete (p)29: end if30: end for31: end for

steps, we have already available a list of all more spe-cific concepts. Before we add them as children of thecurrent concept, we need to eliminate any transitiveclosure if it exists. From the list, any concept that isfound to be more specific than another by lower tran-sitive closure is discarded at lines 16-21, Algorithm 5)and thereafter any remaining more specific conceptsare added as children of the newly-generated closedconcept. Any upper transitive closures as shown inthe steps of Figure 4 are also removed (in line 25-30,Algorithm 5).

2.6 BioLattice compared to CHARM-L

The basic BioLattice algorithm is an intent-extenttree search algorithm similar to CHARM (Zaki &Hsiao 2005). Most closed set mining algorithms in-cluding CHARM only generate intents, but sincein systems biology applications the objects, usuallygenes, are required for visualization, BioLattice gen-erates concepts which have both intents and extents.CHARM-L extends CHARM to include lattice gen-eration, but since concepts do not include extents wedeveloped our own implementation.

BioLattice differs from CHARM-L in terms ofits search technique while visiting branches and alsowhile building the lattice. Figure 1 shows how a Bio-Lattice search tree structures the search space, wherethe top node represents the most general candidateconcept with intents sharing a common prefix of asingle item (e.g., F) denoting an equivalence class foreach of its subsequent specialized concepts.

During the search process, the candidate conceptat the top node can be specialized in two ways. First,by adding extra items to intents obtained from aright sibling, having more weight (see below) and inwhich there is no change in extent (Property 1 & 2).The second case is when the candidate concept sharessome subset of its extent with a right sibling, it canthus be specialized by reduced, i.e., intersected, ex-tents (Property 3 & 4).

21

Intent Concept_idsA C_1,C_2,C_3,C_4,C_5,C_6B C_5,C_6C C_1,C_2,C_4,C_5D C_1,C_3,C_4,C_5,C_6E C_3,C_4,C_5,C_6F C_1G C_2H C_2I C_2

Candidate frequent concept {H,G,A}{g2,g3,g4}More specific concept (H

pG

{C_2

Not subsumed by C_2, thereby, generate new concept_id C_7 and add C_2 as childMore general concept Lr =C_0 (add as a parent)Remove upper transitive closure, as C_2 C_7

)C_0 in b)

C_0 {root}{g1,g2,g3,g4,g5,g6,g7,g8}

C_5{E,D,A,B,C}{g6}

C_4 {E,D,A,C}{g6,g8}

C_6 {E,D,A,B}{g5,g6}

C_3{E,D,A}{g5,g6,g8}

C_2{I,H,G,C,A}{g4}

C_1 {F,D,C,A}{g7}

C_0{root}{g1,g2,g3,g4,g5,g6,g7,g8}

C_5{E,D,A,B,C}{g6}

C_4 {E,D,A,C}{g6,g8}

C_6{E,D,A,B}{g5,g6}

C_3 {E,D,A}{g5,g6,g8}

C_2{I,H,G,C,A}{g4}

C_1 {F,D,C,A}{g7}

C_0{root}{g1,g2,g3,g4,g5,g6,g7,g8}

C_2{I,H,G,C,A}{g4}

C_7{H,G,A}{g2,g3,g4}

C_7{H,G,A}{g2,g3,g4}

a)

b)

c)

Figure 4: Lattice Restructure

Based on Properties 3 & 4, specialized branchesare added under each concept. We propose thatstoring the intersection of the extents Cj〈extent〉 ∩Ci〈extent〉 is sufficient to process branches in the nextrecursive call (see Algorithm 2). Replacement occursstrictly at the prefix and, unlike CHARM, this tech-nique does not require visiting all branches every timeproperties 1 and 2 are satisfied leading to replace-ment of a more general by a more specialised concept,which significantly speeds up the search process. Inbioinformatics domains, especially in our case wheremany genes (or transactions) can share common at-tributes or common subsets of attributes, this com-pression technique not only speeds up search but alsoreduces memory storage requirements.

Thus we have expanded the approach to store ex-tra information while taking advantage of using a con-cept index intersection-based subsumption check. Bi-oLattice checks subsumption at the parent before itgenerates a next level concept, thus building a topdown lattice faster with less restructuring.

3 A web-based browser for BioLattice

One advantage of FCA is that the lattice and formalconcept can be visualized. This hierarchical struc-ture can provide reasoning for classification, cluster,implication discovery, rule learning etc. The problemis that the size of the lattice grows exponentially withthe number of attributes – large numbers of attributesare common in bioinformatics data. Visualization ofsuch lattices in their entirety tend not to be compre-hensible for users (Priss 2006).

We propose an “incremental exploration tech-nique” (Herman, Melancon & Marshall 2000) by plac-ing a visible “window” in the lattice and moving thiswindow along lattice edges to navigate by conceptorder. This is related to previous work on conceptlattice navigation by Godin et al. (1993), Carpineto

and Romano (1996), and Kim and Compton (2004).In common is the idea of displaying only the conceptwith current focus and having link to only the adja-cent concepts (parents or children) in the lattice.

A tabular format is used for intents, extentsand integrated background information, as seen inFigure 5. Links to background information (GeneOntology www.geneontology.org and protein inter-actions www.thebiogrid.org) for each concept areadded to the concept tables when displayed.

3.1 Lattice visualization and navigation

Selection of a concept link from the tabular displayopens an interactive browser page – a snapshot isshown in Figure 5 – to let the user examine conceptswith the following functionality.1. The center of the navigation page has a ‘Main’section that displays the view of a set of gene responseto the corresponding set of stresses for the selectedconcept.2. The group of more specific concepts on the righthand side with the heading ‘More Specific’ representsthe effect of additional stresses (‘more’) in terms ofsensitive genes (‘less’).3. To browse the lattice bottom-up to view moregeneral concepts, the user clicks the link ’more generalconcept’. A ’more specific concept’ link is providedwhen browsing top-down (not shown).4. By default, the more specific concepts are dis-played for the current ‘Main’ concept (i.e, bottom-upnavigation). The link ‘Browse’ when clicked will makethat concept the new focus of the browser.5. Each of the displayed genes has a gene productquery link to the Gene Ontology entry for that gene.6. All concepts have ontology information via the‘GO’ link (not shown). More general or more spe-cific concepts have comparative ontology informationwith respect to the current focus concept. The Gene

22

Figure 5: Concept Lattice

Ontology MySQL database has been integrated withthe lattice browser for this purpose and all three pos-sible ontologies (process, component and function)with significantly over-represented categories are pre-sented.7. A visual display of the concept-related protein-protein interaction network is provided for all the con-cepts via the ‘PPI link’ (not shown). The BioGRIDdatabase has been integrated for this.

Further details on the lattice browser are omitteddue to space constraints and will be published else-where.

4 Case study: yeast systems biology

The problem of understanding the causal mechanismsleading to observable phenotypes in the cell has inrecent times been re-orientated away from single-genemodels to focus more on multiple-gene systems. Thisis driven on one hand by biological need – single genemodels do not explain sufficient functionality – andtechnological innovations enabling genome-wide high-throughput experimental data to be gathered.

Thus focus has shifted to the study of networksas the common representation for biological systems.For example, protein interactions are an increas-ingly important source of information on gene be-haviour (Cagney 2009, Costanzo, M. et al. 2010).and have a potential medical role (Chaudhuri &Chant 2005). Network data are relational, whichcauses problems for standard FCA and machine learn-ing. In this case study we use network data in threetasks to evaluate BioLattice approach and the use In-ductive Logic Programming.

To obtain results on the potential of using a con-cept lattice for evaluation and generation of biologi-cal hypotheses we devised two tasks using a datasetselected for its relevance to the application domain.Data to be mined was acquired from the Saccha-romyces Genome Deletion Project (Winzeler, Shoe-maker, Astromoff, Liang, Anderson, Andre, Bang-ham, Benito, Boeke, Bussey et al. 1999), a set ofyeast strains in each of which exactly one gene fromthe genome has been systematically removed. Biolo-gists have carried out many ’screens’ of the deletantset – selecting a subset of genes and subjecting eachof the corresponding deletants to that stress search-

ing for a ’sensitive’ phenotype that would suggest aThe data set contained 26 such screens for 1094 genesfrom different laboratories.

4.1 Concept ranking by gene interactions

As a first test of the possible biological significanceof the stress combinations in the lattice we ran allgenes in each stress combination against the set ofgenes occurring in the collection of synthetic lethalinteractions at BioGRID (downloaded July 15, 2010).

The cellular systems of an organism can be per-turbed by challenges such as the addition of a stress-inducing agent to the environment or a mutation suchas the deletion of a gene, and this can effect the ob-servable phenotype. The stress data set used in thispaper can be seen as a set of such perturbations,where a cellular system is rendered sensitive to anenvironmental perturbation in combination with thedeletion of a gene. An external reference point forsuch system interactions is the set of “synthetic lethal-ity” pairs of gene deletions, where two genes deletedin combination renders the system unable to survive,although deletion of each gene singly does not havethis effect.

This leads to the following hypothesis: genes im-plicated in stress sensitivity should be more likely toappear in synthetic lethality interactions than genesfrom the complete genome. We used a hypergeomet-ric test (Akand et al. 2010), with a background num-ber of 6140 yeast genes, and 2893 genes occurring ina synthetic lethality interaction. Then for each con-cept in the lattice, we counted the number of genesin a synthetic lethality interaction and the number ofgenes in the concept’s extent, and assessed the proba-bility of seeing that proportion by chance. We found22 concepts with p-value below 1.0 × 10−14, shownin Table 1 ranked in increasing order of p-value. Forinstance, 220 of 249 genes that show the sensitivity“Menadione Fields” are also in a synthetic lethalityinteraction, giving a p-value of 2.4 × 10−44, which islikely to be highly significant.

Since the synthetic lethality test is on a pair ofdeletants, this is an indirect indication of commonfunctionality, but it is not clear what this might be.This leads to the interesting question: if two genes(individual deletants) are sensitive to a stress, are therespective genes more likely to appear in a synthetic

23

Table 1: Concepts ranked by synthetic lethality.p-value Intent – stress sensitivities p-value Intent – stress sensitivities2.4E − 44 Menadione 3.7E − 18 H2O2, Sorbate9.3E − 38 BLM 6.0E − 18 H2O2, Ibuprofen2.4E − 29 H2O2, Menadione 6.8E − 18 H2O2, Mefloquine2.1E − 28 H2O2 7.0E − 18 Mefloquine, Menadione1.6E − 25 Ibuprofen 1.3E − 17 Mefloquine1.7E − 22 BLM, H2O2 5.1E − 17 GHS, homeostasis1.9E − 21 Sorbate 1.1E − 16 BLM, Sorbate2.8E − 21 MMS 2.2E − 16 Menadione, Sorbate1.2E − 20 Ibuprofen, Menadione 1.9E − 15 BLM, Menadione1.4E − 20 TPZ, anticancer 3.9E − 15 H2O2, Ibuprofen, Menadione5.4E − 19 IR2 4.4E − 15 BLM, H2O2, Menadione

GCN4 BAS1 CAD1 MET32 UME6

MET6

Mitochondrial ribosomal small subunit complex

Core Attachment

Transcription factors

MRPS16

MRPS8MRPS17

RSM22

RSM19

RSM25

RSM24

UBP10

Figure 6: Example of a network structure learned for genes in the extent of a formal concept. The structurerelates gene and protein interactions in the mitrochondrial ribosomal protein complex in response to H2O2stress.

lethality interaction ? To test this we compared thenumber of synthetic lethality interactions appearingbetween pairs of genes in concept extents with thosein randomly selected sets of the same size. Applya log-odds ratio, we found a positive score, indicat-ing that 72 (resp. 119) concepts out of over 1300were more likely to contain synthetic lethal pairs thanwould be expected by chance at the 99% (resp. 95%)confidence levels.

This indicates that the concept is likely to denotesome interesting biological function worthy of furtherstudy. It demonstrates how application of an external(to the concept lattice construction) statistical eval-uation criterion can lead to a significant reduction ofthe set of concepts. This makes apparent how post-processing of the lattice can have a dramatic effecton the possible usefulness of the concept set, since alattice of around 100 concepts is much more likely tobe visually navigated, with further analysis applied,than one with an order of magnitude more concepts.

4.2 Relational learning of multiple-stressrules

In this experiment we adopted a machine learningapproach to model dynamic cell behavior in responseto multiple-stress concepts from the lattice. Various

data sets from genomics, protein-protein interactions,transcription factor binding, pathways and the GeneOntology were integrated to learn first order multiple-stress rules. The concept extents containing genessensitive to a common set of stresses comprise thepositive examples while the other data is used as abackground knowledge.A. Genomics data Microarray data on cellular net-work response by yeast to six different environmentalstresses from a study by Causton et al. (Causton, Ren,Koh, Harbison, Kanin, Jennings, Lee, True, Lander& Young 2001) was used in this experiment. Thedata contains the transcriptional response of mRNAlevels in cells observed at 8-10 time points over a pe-riod of 2 hours. Each time series data set under aparticular stress has mRNA levels recorded at irregu-lar intervals following initial exposure to the stressor.We discretized this data from time-courses into thevalues “up” or “down” for each of the conditions.B. Protein-protein interaction data Protein-protein interaction data provides a picture of cellularpathways and cascaded responses in the cell at themolecular level. We used a simplified “flattened” ver-sion of the Gavin et al. (A-C. Gavin and P. Aloy andP. Grandi and R. Krause and M. Bosche et al. 2006)protein complex data. Protein-protein interactionsare represented as true for any pair of genes whose

24

proteins appear in the same core, attachment or mod-ule of one of the stable complexes.C. Transcription factor binding data Transcrip-tion factor binding data defines regulatory networksby indicating transcription factors and their targetbinding genes. Identifying transcription factors thatcontrol gene expression can provide significant insightinto misregulated expression and thereby potentiallinks between transcription (genomics) data and post-translational (protein-protein interaction) data. Forthis work we used a version of the transcription factorbinding (ChIP-chip) data from the study by Harbisonet al. (2004)D. Biochemical pathway data Pathways are an in-valuable resource to understand dynamic cell behav-ior, containing biochemical evidence for a set of in-teracting genes and thereby can unveil interesting re-lationships among them. Yeast biochemical pathwaydata was downloaded from www.yeastgenome.org.E. Ontology data Finally, Gene Ontology (Ash-burner et al. (2000)) data was integrated to re-late all three categories (molecular function, cellularcomponent and biological process) to complete thebackground knowlege required for multiple-stress rulelearning.

4.2.1 Method

We used the Inductive Logic Programming systemAleph 1. The above data types were represented asProlog facts. Since concepts from the lattice containonly positive examples, i.e., of genes sensitive to agiven set of stresses, we used the positive-only learn-ing setting introduced in (Muggleton 1996). The fol-lowing Aleph settings were used for our experiment,where the learning mode is “positive examples only”:maximum number of literals acceptable in a clauseis set to 6; number of randomly generated exampleswas set to be equal to the size of the set of posi-tive examples; minimum number of positive examplesto be covered by an acceptable clause was set to 4;the search strategy was set to be a heuristic best-first(branch-and-bound) search; and the maximum num-ber of clauses to be generated when searching for anacceptable clause was set to 50000.

The following clause was learned for a conceptwhose intent was sensitivity to oxidative stress:

concept(A) :-ppi(B,A,C), tfbinds(D,C),ppi(B,C,E), tfbinds(F,E),ppi(B,A,E).

denotes that gene A, which is sensitive to oxida-tive stress, interacts with two other genes/proteins Cand E that are in the same protein complex. Pro-teins/genes C and E also have interactions amongthemselves, and each of them is bound by transcrip-tion factors D and F. We extracted the set of genescovered by this clause and mapped them onto theprotein complex architecture from Gavin et al. (A-C. Gavin and P. Aloy and P. Grandi and R. Krauseand M. Bosche et al. 2006) to assemble the networkdiagram in Figure 6. In stable protein complexesthose with the greatest degree of functional similarityand physical association are grouped as the “core” or“modules” of a complex, and proteins with greaterheterogeneity are grouped as attachments. Thus anattachment specifies a particular function for a pro-tein complex. Proteins highlighted in Figure 6 as redcircles are sensitive to the oxidative stress (knownfrom the concept definition) and proteins in greencircles are likely to be under the regulatory control

1www.comlab.ox.ac.uk/activities/machinelearning/Aleph/aleph.html

of the transcription factors linked to them by the ver-tical dotted lines.

Interestingly, in one instantiation of the clauseabove, the gene RSM19, which is sensitive to one ox-idative stress in our data set, interacts with RSM22and MRPS17, and RSM22 and MRPS17 also interactwithin the same complex (“mitochondrial ribosomalsmall subunit”). In addition, RSM22 is bound bytranscription factor CAD1 and MRPS17 is bound byGCN4 and BAS1. Although RSM22 and MRPS17were not found to be sensitive to the oxidative stressin the concept intent, they were found to be sensitiveto another oxidative stress, not in the concept fromwhich the rule was learned. This supports the pos-sible inference of this sensitivity from the relationalstructure of the clause as applied to the protein com-plex in Figure 6.

5 Conclusions

In this paper we studied the use of Formal ConceptAnalysis as a framework for visual analytics. We pre-sented a new algorithm for concept lattice construc-tion based on ideas from frequent closed itemset min-ing. This improves on some aspects of previous al-gorithms and has been implemented with a browserinterface as an environment integrating multiple datasources for visual analytics. In the BioLattice systemwe have developed several ways to control concept lat-tice construction to enable better visualization, suchas using a support threshold (preventing concepts be-ing added) and post-processing concepts using exter-nal data sources, particularly relational data, to refinethe concept space. Owing to the highly relational na-ture of the application domain, systems biology, theintegration of machine learning into the visual ana-lytics framework used Inductive Logic Programming.It was shown that domain relevant concepts identifiedfrom the lattice could be used in learning potentiallyuseful rules defining the concept in a first-order rela-tional representation.

Simplifying a concept lattice by selecting a subsetof formal concepts is not as straightforward an op-eration as, say, cutting the concept at a given levelof support (extent cardinality). Owing to the inter-dependence of concepts in the lattice, removal (dele-tion) of one concept will often lead to the need todelete, revise or even add other concepts. To seethis, suppose we have three concepts, each with in-tent containing two out of a possible three attribute,call them A, B and C. The concept to be deletedhas intent {A,B}, while the other two concepts arenot to be deleted. If the concept with intent {A,B}is deleted, however, any other concept whose intentcontains either A or B will also be affected. In previ-ous work (Bain 2003) we developed approaches to in-crementally revise the lattice without reconstructingthe entire Hasse diagram, and this can be viewed asselection of concepts for ontology construction. Fur-thermore, we note that it would be interesting to in-vestigate variant structures of formal concept anal-ysis, such as the concept lattice of the complementof a formal context, and other rough set approxi-mation operators to generate non-closed concept lat-tices (Yao 2004). For example, complementing theformal context can provide information on genes thatare not sensitive to a subset of stresses.

Although the tabular browser interface shown inFigure 5 includes useful functionality, this may be im-proved by adopting a richer graphical interface; thework of Eklund et al. (2009) provides an example ofhigh quality graphics in a lattice browser environ-ment.

25

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26

Combining Ontologies And Natural Language

Wolf Fischer Bernhard Bauer

Programming Distributed Systems,University of Augsburg,

Augsburg, Germany,Email: wolf.fischer | bauer @informatik.uni-augsburg.de

Abstract

Ontologies are a popular concept for capturing se-mantic knowledge of the world in a computer un-derstandable way. Todays ontological standards havebeen designed with primarily the logical formalismsin mind and therefore leaving the linguistic informa-tion aside. However knowledge is rarely just aboutthe semantic information itself. In order to createand modify existing ontologies users have to be ableto understand the information represented by them.Other problem domains (e.g. Natural Language Pro-cessing, NLP) can build on ontological informationhowever a bridge to syntactic information is missing.Therefore in this paper we argue that the possibili-ties of todays standards like OWL, RDF, etc. are notenough to provide a sound combination of syntax andsemantics. Therefore we present an approach for thelinguistic enrichment of ontologies inspired by cog-nitive linguistics. The goal is to provide a generic,language independent approach on modelling seman-tics which can be annotated with arbitrary linguisticinformation. This knowledge can then be used for abetter documentation of ontologies as well as for NLPand other Information Extraction (IE) related tasks.

1 Introduction

In the last years ontological standards (e.g. RDFS,OWL, etc.) have become more and more important.Especially OWL as the de-facto standard for spec-ification of ontologies and logical reasoning has at-tracted many users from different areas, e.g. the re-search community as well as industry. However thesestandards have the following shortcoming: The lackof a clear relationship to natural language. Buitelaaret al. (see [2]) show why a linguistic grounding ofontologies is needed:

• Profound linguistic information in ontologies isneeded for human developers to create moresound ontologies as they are able to better un-derstand the concepts and how they are related.

• An ontology-based information extraction fromtext can rely on the additional natural languageinformation to gather more accurate results whenthe concepts are directly linked to specific lin-guistic information. This also accounts for thesingle components of the overall natural language

Copyright c©2010, Australian Computer Society, Inc. This pa-per appeared at the Sixth Australasian Ontology WorkshopAOW 2010), Adelaide, Australia. Conferences in Researchand Practice in Information Technology (CRPIT), Vol. 122,Thomas Meyer and Mehmet A. Orgun and Kerry Taylor, Ed.Reproduction for academic, not-for-profit purposes permittedprovided this text is included.

process in general. An easy example would bethe use of synonyms or homonyms which some-how have to be related to the specific conceptswithin the ontology. More elaborate exampleswould be metaphors or proverbs, i.e. not onlywords but complete phrasal structures that meansomething else than the single words would im-ply.

• The generation of natural language text from on-tologies needs more accurate descriptions of howontological information can be verbalized.

Moreover the relevance of our tasks is also supportedby the results like e.g. in [8]: NLP interfaces forquerying ontologies are considered to be of best us-age if the user can enter full sentences, although theresults are not as accurate as with a more restrictedand more formal query language. In this case a bet-ter linguistic grounding could probably help to com-bine the advantages of both worlds: The accuracyof a formal standard combined with the comfort ofa natural language interface. In the past, however,the focus of ontological development was clearly laidonto logical formalisms in order to create a best possi-ble reasoning mechanism. Therefore the only way toassociate language related information to standardslike RDFs / OWL is to use the label mechanism.A label allows the association of some simple com-ments to a specific class or property. This is howevernot enough to model all the information necessaryfor a profound linguistic grounding and therefore notsufficient for any sophisticated NLP component, i.e.linguistic substructures or more elaborate grammaticstructures are missing.The approach presented in this paper tries to fill thisgap by using ideas from the field of cognitive linguis-tics. Since OWL does not fulfill all our requirements,we created a customized metamodel allowing the de-scription of both conceptualizations (i.e. the semanticmeaning of a specific domain) and their relationshipsto natural language. As our concept aims towards thecombination of syntax and semantics we have not yetfocused on logical formalisms for reasoning (althoughwe plan to provide a transformation from OWL 2.0to our model in the near future).A first version of this concept has been published in[6]. The contribution of this paper is a stable, genericand powerful way to create ontologies with linguisticinformation being usable by NLP components. Fur-ther the differences to other linguistic standards likeLexInfo, LingInfo, etc. are presented.This paper is structured as follows: First we give amotivation on the overall task and list the require-ments in section (2). Further we delimit this approachfrom related work. The following section 3 describesour concept in detail. Section 4 uses an example to

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show how the different requirements presented in sec-tion 2 can be achieved. Before this paper is concluded(section 6), an outlook is given on how to apply theconcept in a language based system (section 5).

2 Motivation

In this section we give a motivation and define all therequirements our aproach has to fulfill.The most basic question which comes to mind iswhy someone might want to combine semantics andsyntax at all. Humans are good at filling gaps ofany kind, whereas todays software components forsyntactic analysis show promising results. Howevercertain domains are still difficult to automatize, es-pecially those which contain natural language. Al-though state-of-the-art NLP components are sophis-ticated, they still sometimes deliver false or multiple,ambiguous results. Eliminating those errors and am-biguities is often difficult as they rely on additionalsemantic information (e.g. coreference resolution isdifficult to handle without semantic information, thesame accounts for homonyms and synonyms). Allthis information is therefore necessary to create bet-ter computer-understandable representations of text.Those could then be the input for other applications,thereby e.g. relieving the user of manually readingthe text and entering the information on his own.In [2], five requirements have been described whichhave to be fulfilled to linguistically ground an ontol-ogy:

1. capture morphological relations between terms,e.g., through inflection (cat, cats), separatelyfrom the domain ontology,

2. represent the morphological or syntactic decom-position of composite terms and the linking ofthe components to the ontology,

3. model complex linguistic patterns, such as sub-categorization frames for specific verbs togetherwith their mapping to arbitrary ontologicalstructures,

4. specify the meaning of linguistic constructionswith respect to an arbitrary (domain) ontology,

5. clearly separate the linguistic and semantic (on-tological) representation levels.

We are in line with the first four requirements. How-ever we would like to point out some facts on thefifth requirement. Depending on the point of view, aclear separation of the linguistic and semantic levelsmay not be possible. From a computational point ofview a clear separation of linguistic and semantic in-formation may be desirable to efficiently implementthe data structures which manage the different typesof data. Further (from a technical viewpoint) it the-oretically would allow the exchange of e.g. the lin-guistic part in order to add another natural languageto an existing semantic description. However in prac-tice some issues have to be considered: Imagine aknowledge base A, consisting of just an ontology with-out further linguistic information. Now the linguisticinformation of another knowledge base B should beadded to A. The problem is how to establish the con-nections between the linguistic information of B andthe semantic knowledge of A.Today most often just the labels of the different con-cepts within an ontology are used to somehow createa mapping. However knowledge is a very diverse anddifficult structure to capture as it is created within

a humans mind, based on the humans perceptionand experience. Communication is for transportingpieces of this knowledge to other human beings, how-ever the communication itself is ambiguous. Humanstend to generalize specific information, use synonyms,metaphors etc. Due to probably similar experiencesof different humans they have no problem to under-stand what the other persons are saying despite allthe different types of ambiguities.So why is this important to computer science? Incomputer science you try to create systems that arecapable of reacting to the input of humans and of-ten this input comes in the form of natural language,which has exactly these problems as stated above.All these phenomenas are the result of an inseparableunion of language and knowledge. These observations(which have been proven by experiments, e.g. [16],[1]) lead to the question if linguistic and semantic in-formation should be separated in computer science?Or might it be just more effective to use knowledge-bases which treat the linguistic information the sameway they treat semantic information?Regarding the previous example, joining linguisticsand semantics or just the semantics of two knowl-edgebases is a process which has to be done manually(i.e. if a high precision is needed) as long as com-puters do not have a perception of the real world en-vironment. However if the knowledge base consistsof semantic and syntactic information, an automaticmerging could prove to be more effective (i.e. thelinguistic and semantic information of A and B aretreated equally and therefore merged completely), ason the semantic level certain intersections could beidentified which also account for the linguistic partand vice versa.

Therefore, in our opinion, a strict and clear sep-aration of linguistic and semantic representation iswishful from a computational (point of) view but verydifficult from a technical point of view.Besides the five previous requirements, we add twoadditional requirements since the prior ones do notcover certain scenarios completely like NLP.The first one is the grammatical representation, es-pecially in different languages, i.e. certain (sets of)concepts are represented by more complex linguisticstructures (e.g. proverbs). These can not be coveredby a direct one to one mapping of words to concepts.Instead the context of the words as well as their syn-tactic relations are necessary in order to resolve thecorrect meaning. Therefore e.g. complete phrase- andsentence structures must be captured by the linguis-tic model.The second requirement deals with the fact that dif-ferent languages have different grammatics and there-fore different syntactic categories. Therefore the lin-guistic structure has to be easily extensible to coveran arbitrary number of syntactic categories. Thesehave to be combinable in arbitrary ways (e.g. speci-fying that a noun is in plural or singular). This leadsus to define the following two new requirements:

6. Support for complete grammatical structures al-lowing e.g. the statement of proverbs. Thesemore complex grammatical structures have to berelated to their corresponding concepts.

7. Support for an arbitrary number of syntactic cat-egories being combinable in arbitrary ways.

Both requirements can not be fulfilled by e.g. Lexinfo[2] as the linguistic structure seems to be limitedto a certain set of syntactic categories and wordforms (nouns, verbs, adjective) and is thereforenot extensible. Further Lexinfo does not allow a

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more complex modelling of grammatical structuresnecessary for ontological information in complexNLP tasks (as POS tagging, parsing, etc.). Otherstandards like SKOS [10], LexOnto [4] and LingInfo[3] are inferior to LingInfo (as they are not able tofulfill all requirements from 1 to 4 as shown in [2])therefore we will not further delimit these from ourapproach.

2.1 Further Related Work

Other work that is also related to the content of thispaper is the field of Ontology Verbalisation, e.g. [11].This if often done with the usage of Controlled Natu-ral Language (e.g. [7]). Our concept targets a differ-ent approach as we do not want to create naturallysounding text from an ontology but instead create asemantic interpretation from a natural language textwith the help of an ontology. For this process wedo not yet consider logical formalisms and the un-doubted reasoning capabilities given by OWL. How-ever we have to be capable of modeling all differenttypes of natural language varieties. We especially tar-get specific companies and their customer support de-partments. In these domains the number of linguis-tic expressions may vary massively due to differenteducational levels of their customers. Therefore ourapproach has to be more flexible, i.e. it has to covermore linguistic phenomena than are necessary to ver-balise an ontology (normal natural language offersmany ways of expressing a fact, whereas a controlled(i.e. a restricted) natural languages is sufficient toverbalise an ontology).In [12], Richards described a system for requirementsreconciliation using concept lattices. Although the re-sult of their natural language processing step is simi-lar to ours, they use controlled natural language as aninput and do not rely on additional semantic knowl-edge during the ’requirement translation’ process.In the following chapters we develop an approach tolinguistically enriching ontological information satis-fying all the requirements.

3 Knowledge Structure

This section gives an overview of our informationstructure. The diagrams are based on UML.As seen in figure 1, the meta model is separated indifferent Scopes, the three main ones being the Se-manticScope, the SyntacticScope and the Con-structionScope. Scopes are used to model differentaspects of a Domain. A Domain would be e.g. acar manufacturer or a computer seller. Therefore aDomain contains everything that is needed in orderto answer requests which are specific to that certainDomain (even linguistic information).Scopes can be seen as some kind of view onto adatabase (in this case the domain) and not a clearseparation of the data. This way the syntax-lexiconcontinuum stays intact, as all the data is stored in thedomain itself (see e.g. [5], [9]).Moreover it is easier to let experts handle their spe-cific fields without interfering in other experts fields.This way a classic ’domain’ expert can care aboutmodeling and populating the SemanticScope as wellas the SyntacticScope (as he knows which informationcould be represented in which ways) of the Domain.Next, another expert (e.g. a linguist) brings bothworlds together by creating the construction scope.However, in more complicated situations (e.g. the cre-ation of a proverb) the experts could work together.

The three different scopes are described in the follow-ing paragraphs.

Figure 1: Overview of the knowledge base structure

Figure 2: Overview of the generic domain model

3.1 Domain

The Domain is the Scope, which contains all dataof the domain to be modeled. Therefore it acts asa) a container for all the data within the actualdomain as well as b) a reference model for all thedata which can exist within the domain. Therefore adirect combination of different parts of the model ispossible (as described later in this paper).The structure of a Domain is shown in figure 2.Central to the Domain is the ReferencableEle-ment (RE). Everything referencable within the KBis of type ReferencableElement, starting with theRelationship and the Element. The former isused to relate REs with each other. As a Rela-tionship is a RE itself, it can reference other REsas well as Relationships. An Element is a moreconcrete specialization, used to express differentkinds of concepts in later phases. Central to ourKB is the Generalization, which is used in everyScope. It allows the creation of taxonomies in the KB.

3.2 SemanticScope

The SemanticScope is used to model the factualknowledge which is inherent to the actual domain,e.g. specifying that a house consists of walls ora car has an engine. To model this kind of factsthe model sticks to a generic approach. Centralto the SemanticScope are the SemanticElement(SE), the Generalization as well as the Associ-ation. A SemanticElement is a specialization ofthe Domain::Element (seen in figure 3). It is used

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Figure 3: Overview of the SemanticScope of the metamodel

to represent the concepts (in the former example’Car’ and ’Engine’) which are relevant to a specificdomain. An Association is used as a generic mech-anism to relate SemanticElements between eachother. The type of the Association is, opposite toother ontological standards, defined by a SE thatthe Association can reference via the ’isOfType’property. The combination of syntax and semanticsis done by constructions as shown later on.

3.3 SyntacticScope

The SyntacticScope (figure 4) references all theForms used to represent the actual concepts, e.g.the SemanticElement ’Car Body’ could be referencedby the actual Forms ’Car’ and ’Body’. Therefore,the SyntacticScope contains the SyntacticElementat the top. This is inherited to the Form as wellas the SyntacticCategory. A Form will actuallyrepresent the different strings (e.g. ’Car’ or ’Body’;more in section 4). Each Form can further beassociated with a SyntacticCategory (e.g. ’Noun’,’Verb’ etc.). A SyntacticCategory itself can referenceother SyntacticCategories (e.g. a ’Verb Plural’category could reference ’Verb’ and ’Plural’). Thisis in alignment with the fact that different culturesuse different SyntacticCategories, therefore we caninclude an arbitrary number of them. However it is avery time consuming task to add every possible formof a word (just think of verbs and their different formsthroughout different times like go, went, gone etc.).Therefore there is a more generic way to representforms, i.e. the root of a word (FormRoot). Thiswill serve as the basis for a collection of differentforms of the same word. A FormRoot can furtherdirectly associate its more specific full forms.

3.4 ConstructionScope

The ConstructionScope (figure 5) contains all the in-formation necessary for combining the SemanticScopewith the SyntacticScope. This is done by Construc-tions. A Construction contains Symbols and State-ments, which impose restrictions on the Symbols. A

Symbol can either be a SemanticSymbol (referenc-ing a SemanticElement), a SyntacticSymbol (refer-encing a SyntacticElement) or a ConstructionSym-bol (referencing a Construction). Basically, a Symbolcan be seen as a variable in a programming language:The referenced Element presents the type of the vari-able, whereas the name of the Symbol is the name ofthe variable. In the example section, we use the no-tion Car(c), which would be a SemanticSymbol c ofthe type Car.To create a mapping between a SemanticSymbol anda SyntacticSymbol (i.e. actually associate a Seman-ticElement with a SyntacticElement), one simply hasto create a Construction which contains the corre-sponding symbols. This allows to map a certainSyntacticElement to a SemanticElement. Also, moreelaborate structures and mappings can be created thisway by restricting e.g. the order of the single wordswith a specific Statement.To describe more elaborate grammatical structures(e.g. the order or the type of words), there can befurther specifications (so called Statements) on thereferenced Symbols. A Statement is further special-ized into a ConditionStatement, an EffectState-ment and a hybrid form, the ConditionEffect-Statement. During runtime first all ConditionState-ments of a Construction are evaluated and then (ifall are true) all EffectStatements are executed. TheseStatements are basically functions which are calledwith a certain number of arguments (the Symbols).As the name implies, ConditionStatements checks ifcertain restrictions hold for the current context a con-struction may be applied to. EffectStatements canadd additional information to the current context ifall conditions are met. The ConditionEffectStatementdefines a hybrid type of the latter two which bothchecks a specific condition and uses this informationto immediately add the effect to the current solutionpossibility without waiting for the result of the re-maining ConditionStatements.Statements are our way of specifying how the infor-mation of the text should be composed, thereby lead-ing to compositional semantics. This should becomeclearer during section 4.

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Figure 4: Overview of the SyntacticScope of the metamodel

Figure 5: Overview of the ConstructionScope of the metamodel

4 Example

In this section we will provide an example of howour ontology can be annotated with linguistic infor-mation. As the central theme for this section wehave chosen a car domain (described in figure 7). Itcontains a simple car concept, which consists of a carbody. The car itself is further driven by a person.Table 1 presents different linguistic information andhow they exist within the syntactic scope (therebyfulfilling 7), as an arbitrary number of syntacticcategories can be added). The first column is aunique ID, the second column depicts the type ofthe corresponding row (C for syntactic category, Ffor form and FR for form root), the third column

is the actual value of the row, the fourth columnmarks the form root (if the row is of type form)and the last column contains references to all thesyntactic categories the form (root) actually canrepresent. Note that these are mutually exclusive,i.e. in an actual text one form can represent onlyone of the referenced categories (the selection of thecorresponding syntactic category is made duringruntime and depends on the context of the word).As can be seen in this small example, a generic wayof modeling linguistic data is available. Therefore,requirements 1 and 4 from section 2 are fulfilled.Figure 6 depicts how constructions can be arrangedwithin a hierarchy. A very generic constructionis put on top of the ’tree’ and then spezialized in

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other construction types. In this small excerpt theconstruction was endetailed by a construction typedescribing generic mapping constructions and an-other one presenting phrasal structures. A mappingconstruction in this case does what the name implies:It maps a syntactic representation to a semanticconcept. This is further defined in section 4.1. Aphrasal construction on the other side is used todescribe more complex grammatical structures (moredetails can be seen in section 4.2).

Figure 7: A small excerpt of the semantic scope of acar domain

Table 1: Small excerpt of a syntactic scopeID Type Value FR Cat

1 C Noun - -

2 CNoun

Singular- -

3 CNounPlural

- -

4 FR Person - 1, 2

5 F Person 4 2

6 F Persons 4 3

7 F Car - 2

8 F Body - 2

4.1 Mapping Construction

The first and most simple construction is one whichmaps one concept to a single word (seen in table 2):The syntactic representation of a car (represented inthe table by the function CarForm and ’stored’ inthe variable cf) is mapped to the semantic conceptcar (represented in the table by the function Car andstored in the variable c). This mapping is made bysimply referencing the two symbols c and cf withinone construction as seen in table 2.

Table 2: Construction for mapping a SemanticEle-ment to its forms

Attribute Content

Name: ’Car’ MappingSyntactic Symbols: CarForm(cf)Semantic Symbols: Car(c)Construction Symbols: -Condition Statements: -Effect Statements: -

In order to fulfill requirement 2 the semantic ele-ment ’Car Body’ is represented by the composite term’carbody’ (shown in table 3). Again several syntac-tic and semantic symbols are created first. Therefore,the forms CarForm and BodyForm are referenced.

The mapping between these syntactic symbols andthe corresponding semantic concept CarBody is im-plied by all three of them being referenced by theconstruction. Additional information is however nec-essary on how the different symbols within have tobe treated. Therefore, two condition statements areused. The first statement specifies the order of thesymbols within the text (meaning that the ’CarForm’should actually come in front of the ’BodyForm’) andthat the both symbols should also be treated as onesingle word (i.e. ’carbody’ and not ’car body’). Otherstatements can be thought of which allow both repre-sentations (i.e. as a single or as two terms). Thereforerequirement 2 is fulfilled.

Table 3: Construction for mapping a concept to acomposite form

Attribute Content

Name: ’Car Body’ MappingSyntactic Symbols: CarForm(c), BodyForm(b)Semantic Symbols: CarBody(cbsem)Construction Symbols: -Condition Statements: InOrder(c, b), CompositeTerm(c, b)Effect Statements: -

4.2 Phrasal Constructions

This section describes more complex constructionsused to specify grammatical structures. A first ex-ample is given in table 4. It specifies a noun phrase,consisting of an article, adjective and noun. There-fore, three constructions are referenced (m1, m2 andm3). For the first one, the condition must hold thatit contains the category type ’Article’, the second an’Adjective’ and the third a ’Noun’. Further, all threehave to be ordered as m1, m2 and m3. The last state-ment IsRelated checks the semantics of the given ar-guments. Therefore it checks if the meaning of con-struction m2 (representing the adjective) is related tothe meaning of m3 (the construction, representing thenoun). If all conditions can be evaluated at true, theeffect statements are executed. HasAttribute createsas a result two elements (only if they do not exist yet)m3 and m2, where m2 is referenced from m3 withan attribute relation (i.e. a relation referencing theSemanticElement ’Attribute’). RepresentsCategoryadds the given category to the construction duringruntime, in this case a simple ’NounPhrase’ construc-tion.

Table 4: Construction for a noun phraseAttribute Content

Name: Article + Adjective + NounSyntactic Symbols: -Semantic Symbols: -

Construction Symbols:Construction(m1),

Construction(m2), Construction(m3)

Condition Statements:

IsOfType(m1, Article),IsOfType(m2, Adjective),

IsOfType(m3, Noun), InOrder(m1,m2, m3), IsRelated(m2, m3)

Effect Statements:HasAttribute(m3,m2),

RepresentsCategory(NounPhrase)

The final example (as seen in table 5) uses thepreviously defined constructions for specifying a com-plete sentence structure, further indicating a simpleverb-argument structure. It consists of a noun phrase(np1) → verb phrase (vp, specified accordingly tothe NounPhrase construction)→ second noun phrase

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Figure 6: A small excerpt of a possible construction hierarchie for an English domain

(np2). The construction specifies that the meaningof np1 must be related to np2 by the meaning of vp(stated by SearchTriple). In addition the syntac-tic parts of noun phrase 1, the verb phrase and nounphrase 2 have to come in order. If all these conditionscan be met, a new triple is inserted into the interpre-tation model, consisting of two nodes (the meaning ofnp1 and np2) and a relation with the type of the vpmeaning.Constructions 4 and 5 fulfill requirements 3 and 6.

Table 5: Construction of a simple verb-argumentstructure

Attribute ContentName: NP + VP + NPSyntactic Symbols: -Semantic Symbols: -

Construction Symbols:Construction(np1),Construction(vp),Construction(np2)

Condition Statements:

IsOfType(np1, NounPhrase),IsOfType(vp, VerbPhrase),

IsOfType(np2, NounPhrase),InOrder(np1, vp, np2),

SearchTriple(np1, vp, np2)

Effect Statements:CreateTriple(np1, vp, np2),

RepresentsCategory(Sentence)

5 Application and Outlook

The initial motivation behind this concept was to de-velop a system which creates semantic interpretationsfrom text. This system uses the POS tagging capa-bilities of the Stanford Parser and takes the result-ing syntax tree to create a semantic interpretationof the text which is in alignment with the ontology.As we partly have ’outsourced’ the syntactic analysisto another system this is not a fully parallel analy-sis approach but relies on a state-of-the-art compo-nent in the beginning of the process. The rest of theprocess however (dependency parsing, semantic in-terpretation construction) is done in parallel (whichis partially in line with e.g. FCG [13], [14], [15]). Thesystem can identify ambiguities and problems at anearlier stage which can lead to better results. Theprototype therefore takes an ontology (based on theconcept described in 3) and a natural language text.It lets the Stanford Parser analyze the text and thenapplies the set of available constructions to the syn-tax tree in a bottom-up approach. Therefore it firstmatches the single mapping constructions to the textand continues to add more elaborate constructions.A first prototype is running and an early result canbe seen in figure 8. It depicts an interpretation ofthe sentence ’The car is driven by the CEO’. The

blue entangled area is the actual semantic interpre-tation. Elements with the prefix ’Mapping’ are con-structions which just map a syntactic to a semantic el-ement, ’SynSym’ means ’Syntactic Symbol’ and ’Con’is short for construction. Only the entangled elementsare relevant to understanding the text, the remainingelements are just additional elements which were con-structed during the analysis process.In the near future we will work on different aspectsof the project. One is the current interpretation algo-rithm, which at this moment is just a simple greedyone. However we are going to implement an evolu-tionary algorithm as we think that it might providebetter results in bigger and more complex scenarios.Further a big challenge is the amount of linguisticinformation needed to parse text. Due to the usageof the Stanford Parser this problem has declined abit in its importance. A third part is to incorporatemachine learning methods into the overall process.

6 Conclusion

In this paper we have given a motivation why alinguistic enrichment of ontologies is necessary andwhich are the exact requirements. Further we haveshown how we think all the given requirements canbe fulfilled. Our idea focuses on the usage of ontolog-ical knowledge for NLP based scenarios opposite toother approaches, therefore connecting the syntacticwith the semantic world.Currently a framework is created on top of the meta-model to parse text with respect to the domain knowl-edge. First results are very promising and work onthis concept will be continued.

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[2] P. Buitelaar, P. Cimiano, P. Haase, and M. Sin-tek. Towards linguistically grounded ontolo-gies. In Proceedings of the 6th European Seman-tic Web Conference (ESWC09), pages 111–125.Springer.

[3] P. Buitelaar, T. Declerck, A. Frank, S. Racioppa,M. Kiesel, M. Sintek, R. Engel, M. Romanelli,D. Sonntag, B. Loos, et al. Linginfo: Design andapplications of a model for the integration of lin-guistic information in ontologies. In Proceedingsof OntoLex 2006. Citeseer, 2006.

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Figure 8: Interpretation example of the sentence ’The car is driven by the CEO’

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[5] W. Croft. Radical construction grammar: Syn-tactic theory in typological perspective. OxfordUniversity Press, USA, 2001.

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[7] K. Kaljurand. Attempto controlled English as aSemantic Web language. 2007.

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Comparison of thesauri and ontologies from a semiotic perspective

Daniel Kless, Simon Milton Department of Information Systems

University of Melbourne 111 Barry St, VIC 3010, Australia

{klessd,smilton}@unimelb.edu.au

Abstract Thesauri are frequently stated or indirectly treated as subtype of ontologies or vice versa while other definitions explicitly distinguish them. To encounter the lack of clarity this paper provides an in-depth comparison of these types of models. The comparison followed a semiotic approach and considered syntactic, semantic and pragmatic differences between ontologies and thesauri. For the comparison data models of thesauri and ontologies were produced that – in contrast to existing meta- and datamodels – are comparable with each other. The analysis revealed significant differences in the semiotic aspects of thesauri and ontologies. This finding challenges the treatment of ontologies and thesauri as type of one another. The comparison presented in this paper shall also provide input for standardization efforts in clarifying the relatedness of thesauri and ontologies. Keywords: ontology, thesaurus, comparison .

1 Introduction

The motivation of this paper lies a personal journey of the first-named author: In 2004 he commenced studying a Masters program in “Content and Knowledge Engineering” at the University of Utrecht1

From mid 2005 on he wrote his Master thesis in a company, where his goal was to develop methods and strategies to maintain and improve a specific ontology used in knowledge management. Weeks of literature review revealed various methods for ontology engineering (Fernández-López & Gómez-Pérez 2003) and ontology evaluation (Hartmann et al. 2005). All of these appeared to be of little practical use for guiding the further development of the specific ontology in place. Generally spoken, the methods often appeared too general and it was also hard to grasp, if and how the knowledge in the ontology papers could be related to the domain-specific ontology.

. The study program covered and still covers aspects of representing knowledge and organizing information. Ontologies were as much on the agenda as they are in many other universities today.

The insight settled that practical guidelines for developing ontologies still need to be developed. Some colleagues, who studied information science, gave him

Copyright © 2010, Australian Computer Society, Inc. This paper appeared at the Sixth Australasian Ontology Workshop AOW 2010, Adelaide, Australia. Conferences in Research and Practice in Information Technology (CRPIT), Vol. 122. Thomas Meyer and Mehmet A. Orgun and Kerry Taylor, Eds. Reproduction for academic, not-for-profit purposes permitted provided this text is included.

the hint to look at the thesaurus standards (ISO 2788 1986; ISO 5964 1985; Aitchison et al. 2000). He soon realized that new versions of these quite old standards have been partially released as British Standards (BS 8723 2005). These standards did not only answer his research question, but also did they address practically highly relevant topics that exceeded his expectations by far, e.g. principles of vocabulary control, guidelines for the form of terms, structural relationships, dealing with complex concepts (multi-word terms), facet analysis, presentation and layout, managing construction and maintenance, multilingualism, a data model and formal languages for exchange. From this point on he wondered whether the company’s ontology should not be better called a thesaurus.

The case raises the fundamental question of what is the difference between a thesaurus and an ontology. This question is relevant to address since it is prerequisite for answering numerous other questions such as how a given model can be unambiguously classified as an ontology or thesaurus, whether ontology literature can be applied to constructing and evaluating thesauri and vice versa, whether the described experience was an unfortunate personal one or whether the confusion is a common problem.

The comparison of thesauri and ontologies shall also be subject of an ontology chapter in part 2 of the currently developed international thesaurus standard ISO 259642

Thesauri and ontologies are both relevant approaches to modelling domains, each for different reasons: thesauri exist for many subject fields

. Part 2 of that standard aims at establishing interoperability between thesauri and other vocabularies for information retrieval. Practically this means mapping thesaurus elements to elements of other vocabularies. Besides the questions of what are differences between thesauri and ontologies, questions arose such as whether an ontology can be considered a vocabulary at all.

3

Goal. The quality of an international standard as well the ambition to truly understand the ground of what is a thesaurus in contrast to an ontology requires an in-depth insight into the philosophy, nature, structure, semantics and application of thesauri and ontologies. Moreover, a comparison needs to be easy to understand for humans. The focus on humans is opposed to initiatives that compare models in a more formal and machine-readable

whilst ontologies – in particular their description language OWL – are considered a central element in the Semantic Web vision and are becoming increasingly popular.

1 http://www.informationscience.nl/ 2 http://www.niso.org/workrooms/iso25964 3 Overview in: http://www.taxonomywarehouse.com/

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way in order to support automated functions such as the conversion of models into each other, e.g. the Ontology Definition Metamodel (OMG ODM 2009).

Section 2 provides a brief overview of current comparisons between thesauri and ontologies. Section 3 outlines the method for how the described goals shall be achieved. Sections 4 and 5 will apply this method to describe thesauri and ontologies. Based on these descriptions section 6 will compare thesauri and ontologies with each other before section 7 will discuss implications from the comparison. Section 8 draws conclusion from the comparison.

2 Existing comparisons Thesauri and ontologies have rarely been compared in depth and detail. The comparisons are either too superficial to serve deep understanding (Gilchrist 2003; van Rees 2003), describe thesauri and ontologies without truly relating them to each other (Garshol 2004; Uschold & Grüninger 2004; Beck & Pinto 2003) or have an unclear or questionable notion of what an ontology is (Fischer 1998).

Further, there are attempts of converting thesauri into ontologies, e.g. the ASFA/Agrovoc thesaurus (Sabou 2007, sec.5.5 and 5.6), the MeSH controlled vocabulary (Soualmia et al. 2004) or the Gene Ontology (Wroe et al. 2003). In pursuing semi-automatic conversions these attempts imply mapping between thesaurus and ontology elements, but are not a comparison of them as such.

Finally, there is the “Simple Knowledge Organization Systems” specification that describes itself as a “standard, low-cost migration path for porting existing knowledge organization systems to the Semantic Web” (W3C SKOS 2009). A thesaurus is such a knowledge organization system and SKOS can be used to describe thesauri. The SKOS specification relates to OWL elements, but is neither a conversion of thesauri to ontologies nor a comparison of the two.

Overall, there is no literature that describes the differences and commonalities of thesauri and ontologies in an insightful, but still easily comprehensible way – a gap that will be addressed in this paper.

3 Comparison method The comparison of thesauri and ontologies was approached in several steps:

1. Selecting comparison criteria 2. Choosing reference points defining a thesaurus and

an ontology 3. Choosing a consistent presentation style 4. Describing thesauri and ontologies independently by

comparison criteria and common visualization style 5. Comparing thesauri and ontologies by criteria

The following subsections detail these steps.

3.1 Comparison criteria: semiotics as a lense For an in-depth comparison of ontologies and thesauri, it turned out to be useful to take a semiotic perspective. From such point of view thesauri and ontologies are artefacts that consist of signs. Price & Shanks (2005) distinguished three logical components of a sign and traced back their historic development: (1) the form/

representation/ syntax of a sign, (2) its meaning / referent and (3) its use / interpretation. As figure 1 illustrates relations can be established between the forms of two signs (syntactic relations), between its form and meaning (semantic relations) as well as between its meaning and use (pragmatic relation). Rules for syntactic relations are often manifested in a grammar or a metamodel that defines the structure between representations. Representations and syntactic relations together form a language or a model.

Figure 1: Semiotic framework

3.2 Reference points There are several viewpoints of what thesauri and ontologies are. This paper will generally refer to international standards specifying thesauri and ontologies.

In terms of ontologies we will refer to the Web Ontology Language OWL. Its specification is published in a 2nd version by the World Wide Web Consortium (W3C OWL 2 Overview 2009). In particular, we will refer to OWL’s “Structural Specification and Functional-Style Syntax” (W3C OWL 2 Syntax 2009) and the “Direct Semantics” (W3C OWL 2 Direct Semantics 2009). The motivation for referring to OWL is that it has gained considerable attention – not only through Semantic Web activities, but also through other disciplines such as Knowledge Management and Biomedicine. Particularly its basis on web languages (RDF and XML) and its exchange over the Internet may have been and may still be reasons for that development.

The British standard “Structured vocabularies for information retrieval. Guide” (BS 8723 2005-2008) will be used as a reference point for thesauri. This standard has been published in five parts of which part 2 “Thesauri” and part 5 “Exchange formats and protocols for interoperability” are of particular importance for this paper. Referring to the British Standard BS 8723 is justified since it succeeds the relatively aged international thesaurus standards ISO 2788 (1986) and ISO 5964 (1985). Moreover, BS 8723 has been the input for part 1 of the currently developed international thesaurus standard ISO 259644

With respect to the usage of thesauri and ontologies, this paper focuses on very stereotypical and original cases only that have been proven and demonstrated over time instead of presenting visions and prototypical projects.

. There are other national thesaurus standards such as the US American one (ANSI/NISO Z39.19 2005).

4 http://www.niso.org/workrooms/iso25964

Form (representation, syntax)

Meaning (referent)

Pragmatic relations

Semantic relations

Use (interpretation)

Syntactic relations (grammar, structure)

Language, Model

Semantics

Usage, Applications

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3.3 Presentation style In order to compare the syntax and syntactic relations, it is useful to visualize them. UML class diagrams have become the de-facto standard for depicting such computer artefacts and to support human understanding. UML was used in the British thesaurus standard to provide a conceptual data model for thesauri (BS 8723 Data model 2008; BS DD 8723-5 2008). In OWL UML is used to support the specification of the structure of the language in form of a metamodel (W3C OWL 2 Syntax 2009). In both cases the usage of UML is meant to provide similar insights into the structure of an ontology and a thesaurus.

Nevertheless, the usage of UML in OWL differs from the one in the thesaurus standard. While OWL uses the multiplicities at the end of UML associations for indicating the number of arguments allowed in an OWL statement, the thesaurus standard indicates the number of target instances that may be associated with a single source instance across the given association with the multiplicities. The metamodel in OWL describes the syntax and structure like a programming language while the thesaurus standard describes a data model for thesauri. Another perceivable difference is that OWL only makes use of (directed) UML associations since it aims at indicating the parameters of the functional language elements. In contrast, the conceptual data model in the thesaurus standard also uses UML composition connectors, which is usual for data modelling. These differences in using UML make it very difficult to compare an ontology and a thesaurus based on the original UML models. The approach chosen in this paper was to remain the UML datamodel for thesauri and to adapt the OWL metamodel to a datamodel representation.

Finally, there are subtle variations in UML modelling and the capabilities of UML modelling tools. This paper will adhere to the way Bennett & Skelton (2001) explain UML modelling elements and their usage. In particular, UML association classes for n-ary associations will be used. The multiplicities indicated at the end of these n-ary associations were extended by indicating inner and outer multiplicity as suggested by Génova et al. (2002). Visual Paradigm for UML5

Both, semantics and uses of ontologies, were described in text form – former through definitions, latter by using examples from a dummy domain of “family structure”. The explanation of semantics in text form does not have OWL’s formality and precision (W3C OWL 2 Direct Semantics 2009). Nevertheless, such formal specification is not applicable to thesauri. A human-readable explanation of the semantics using examples is better suited for the goal explained in the

is one of the few tools that supports modelling n-ary associations in such way and was chosen for creating the UML diagrams presented in this paper.

introduction.

3.4 Description of thesauri and ontologies Thesauri and ontologies were modelled with respect to the three semiotic aspects (syntax, semantics, use). More precisely, the comparison is always on the relations between these elements (structure/syntactic relations, semantic relations, pragmatic relations, see figure 1).

5 http://www.visual-paradigm.com/product/vpuml/

The transformation of the ontology metamodel into a datamodel was done manually and practically included two phases: (a) building up a new, independent model based on reading through the W3C OWL 2 Primer (2009), (b) comparing and refining that model with the existing OWL 2 metamodel and its syntax specification (W3C OWL 2 Syntax 2009). This approach did not only produce an UML model comparable to the one for thesauri, but also – and possibly even more importantly – provided a deep understanding of the nature of OWL-based ontologies. Especially the examples provided in the OWL 2 primer provided insights that are beyond what is presented in existing thesaurus-ontology comparisons (see section 2). A protocol captured various questions and issues that arose while re-modelling. These questions were sometimes answered through the help of additional ontology or UML modelling literature and led to decisions added to the protocol.

The length of this paper required to restrict the presented ontology and thesaurus details to a) the fundamental groupings of syntactic elements and b) those elements that are necessary to compare thesauri and ontologies. The UML diagrams in this paper reveal only for latter elements how they are related to other elements through UML associations in sections 4 and 5.

The three semiotic levels were tried to be explained separate from each other. Nevertheless, due to the goal of human understandability, the definitions of thesaurus and ontology elements and thus part of their semantics will be explained in the syntactic sections. The sections about the semantics address the bigger semantic picture.

3.5 Comparison of thesauri and ontologies The comparison of thesauri and ontologies that is presented in section 6 aimed at comparing the thesauri and ontologies with respect to their semantics and use –more precisely: their semantic and pragmatic relations. A direct comparison of the structure/syntactic relations was neglected since it does not provide any useful insights isolated from its semantics. The semantic matching happened in several steps:

a) Identification of ontology elements that have no correspondent thesaurus element and vice versa

b) Identification of ontology and thesaurus elements, which definitions fully match

c) Identification of approximate matches of elements and discussion of necessary actions to match them

For comparing the use of thesauri and ontologies it turned out to be useful to consider the entire process chain from developing thesauri and ontologies until their means-to-an-end usage. Superficially comparable phases were mapped and their differences argued in the light of the underlying semantics for thesauri and ontologies each.

4 Ontologies

4.1 Structure Four fundamental groups of syntax elements can be distinguished in the OWL specification: entities, expressions/restrictions, axioms and annotations. They will be introduced in the following subsections.

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4.1.1 Entities Entities are the fundamental ontological building blocks of ontologies. The most important ones are detailed in figure 2 and include: • Named individual... actual objects or subjects from the

domain, e.g. Roger Federer, Myla Rose • Class... abstract representation of a set of individuals,

e.g. man, person, family • Data property... attribute of individuals, e.g. date of

birth, sex • Object property... relationship between two

individuals, e.g. being married to..., being a child of... • Datatype... abstract representation of a set of values,

e.g. strings, decimal numbers Object properties and also data properties can have various characteristics. They can be functional, inverse functional, transitive, symmetrical and reflexive. Such properties are displayed as UML attributes of data- and object properties in figure 2 and are considered axioms in the OWL specification.

Figure 2: UML datamodel for ontologies

(excerpt of thesaurus-relevant elements only)

4.1.2 Expressions Most entities are never referred to directly, but through expressions that are supertype of these entities: individual, class expression, object property expression or data property expression being supertype of named individual, class, object property or data property (not displayed in figure 2) respectively.

Expressions/restrictions function is to define new entities or to restrict existing ones – generally by relating to other entities. The biggest variety of such expressions/ restrictions exists for classes; there are just few for object properties and datatypes. In particular the following groups of class expressions can be distinguished: • Propositional connectives… the union, intersection or

complement of existing classes • Enumeration of individuals… pointing out individuals • Object property restrictions… limit the way a class

can relate to other classes through object properties • Data property restrictions… limit the way data

properties can be used

4.1.3 Axioms Axioms are statements about the relatedness of entities. Corresponding to the variety of entities, class axioms, object property axioms, data property axioms, datatype definitions and assertions (relating to individuals) can be distinguished. Axioms that are relevant for comparison with thesauri are: • Subclass of: all properties that account for a class

account to its subclasses as well, e.g. A man is a person

• Class assertion: an individual is declared to be a member of that class and has its properties, e.g.

. (class) (subclass axiom) (class)

Roger Federer is a Person

4.1.4 Annotations

. (individual) (class assertion) (class)

Annotations are human-readable labels that can be attached to entities, axioms or ontologies as a whole. They are formed out of an annotation property and an annotation value. Depending on the annotation property annotation values can be literals of a defined datatype or IRIs. An IRI is an acronym for Internationalized Resource Identifier and is basically a string that follows a strict nomenclature.

4.2 Ontology semantics When modelling domains with ontologies, three metalevels can be distinguished (see table 1). The first metalevel is the ontology language itself, which provides a specification of syntax, structure and semantics. The second metalevel is a vocabulary for a specific domain. The vocabulary is specified using the classes, properties, axioms and expressions of the ontology language and expresses abstract knowledge about the domain of discourse. The third metalevel uses the specified vocabulary to make statements about the domain’s objects using the assertions of the ontology language. This can be seen as expressing knowledge about real-life objects in the domain. With other words: the specified

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entities in the 2nd and 3rd metalevel are instantiations of the entities in the previous metalevel each. The expressions/restrictions and assertions are instantiated to specify the entities in the respective metalevel.

Metalevel Described entities (examples)

Specification means

Example statement in specification

Ontology language

Individual Class Object property Data property

Syntax Structure Semantics

Subclass axioms relate a class to at least one other class.

Domain vocabulary

Man (class instance) has child (object property instance) has birth day (data property instance)

Expression/ restriction Axiom

A man is a person. (subclass axiom)

Domain objects

Roger Federer (individual instance)

Assertion Roger Federer has child Myla Rose. (object property assertion)

Table 1: Metalevels of ontology modelling

A further important aspect of ontology semantics is its so-called open-world assumption. It basically means that missing knowledge statements are considered neither true nor false, but simply unknown. For example, if in a relatively complex ontology about family structures there is no statement that persons are either man or woman, this does not mean that reality is or is not like that. It is simply nothing known about it. Another implication of the open-world assumption is that ontology statements can exist independently from the rest of the ontology or the ontology as a whole.

It is also important noting that the explained semantics in an ontology do not require human language. The labels that that can be assigned to entities in form of annotations simply make it somewhat easier for humans to build an ontology. From a semiotic perspective they are the syntactic side of signs. In the context of an ontology the annotations are informative and do not have any semantic meaning. Instead, all entities as well as an ontology as a whole have the possibility to be assigned an IRI by which they can be uniquely referenced internally and externally. Also the examples presented in this paper use natural language only for better understandability. Ontology without labels form perfectly valid ontologies.

4.3 Ontology usage While there are various claims of what ontologies are good for, the original design goal of ontologies is to reason about the described knowledge. Antoniou & van Harmelen (2009) list efficient reasoning support as one of the main requirements of ontologies and give examples of what reasoning support can be used for: • Inferring class membership for individuals • Inferring equivalence of classes • Checking the consistency of an ontology (rather an

evaluation issues for ontologies than a usage of them) These generic benefits of reasoning algorithms can be translated into domain-specific applications, e.g. in the medical field: • Measuring various symptoms of a patient (individual)

and inferring the disease from that information • Discovering the relatedness of two diseases based on

the knowledge described in an ontology

5 Thesauri

5.1 Thesaurus structure A thesaurus contains the following main elements: • Concept… unit of thought, e.g. the notions of a man,

person or family • Term… word or phrase used to label a concept, e.g.

“man”, “male adults”, “person”, “family” • Relationship… relationship between concepts which

is inherent in the concepts themselves (see examples in section 5.2)

• Note… information about a term or concept (internal or user-oriented), e.g. a definition or scope note about what is a family (with respect to the thesaurus scope)

Figure 3 reveals the relatedness of thesaurus elements. One single preferred term and optionally more non-preferred terms can be assigned to a thesaurus concept. For historical reasons, equivalence relationships are defined between the preferred term and the non-preferred terms – a redundant information since all terms are assigned to a single concept. Associative and hierarchical relationships can be defined between concepts. Scope notes can be provided for concepts; definitions and editorial notes can be stored for terms; history notes can be captured for concepts and terms. Plenty more internal information is captured for most thesaurus elements, e.g. the contributors for the thesaurus as a whole or the creation date. Such elements are indicated as attributes of the UML classes in figure 3. The role attribute in a thesaurus relationship allows specifying subtypes of the respective relationship. With respect to mappings to ontologies the pre-defined subtypes of hierarchical relationships will be relevant (see section 6.1).

Figure 3: Relations between selected syntactic

elements in thesauri

Further optional elements in a thesaurus are facets. Facets are groupings of concepts of the same inherent. They group hierarchically subordinated concepts and explain, which characteristic of division forms these groups, e.g. subordinated concepts for a concept ‘person’ could be

39

grouped by sex, nationality or age. Such facets are presented as so-called node labels. They are different from and cannot be used as terms. They are simply an aid for thesaurus navigation and structuring.

Another supplementary thesaurus feature is the distinction of simple and compound non-preferred terms and the relationship that can be established between those two – the compound equivalence. This feature allows indicating that a combination of simple concepts (e.g. family and psychology) is to be used to express the idea of a specific concept (e.g. family dynamics). This supports a typical characteristic of thesauri: expressing the subject of a work through a combination of concepts that constitute a complex and specific idea (see also section 5.3).

5.2 Thesaurus semantics The departure point for constructing a thesaurus is typically the terms of a domain. Terms with equivalent meaning in a language are assigned to the same concept and associated through equivalence relationships. One term is chosen as the preferred term to express the meaning of a concept. Terms with the same spelling, but different meanings are disambiguated through qualifiers (qualifiers in brackets just right after the term). Scope notes for the concept and definitions for the terms further contribute to the meaning. Ultimately, the structure of a thesaurus, particularly the hierarchical relationships, contributes to expressing the meaning of a concept (BS 8723-2 2005, chap.5). In this sense the structure can be roughly seen as the “sense context” of a concept.

The thesaurus standard provides somewhat ambiguous definitions for its two relationships: • Hierarchical relationship: the scope of one

(narrower) concept falls completely in the scope of another (broader) concept; must be one of the following (BS 8723-2 2005, sec.8.3): − Generic relationship (NTG/BTG): link between a

class or category and its members or species, e.g. person NTG man

− Whole-part relationship (NTP/BTP): link between a whole and its exclusive parts, e.g.

(concept) (narrower term, generic) (concept)

name NTP surname

− Instance relationship (NTI/BTI): link between a general class of things or events, expressed by a common noun, and an individual instance of that class, often represented by a proper name, e.g.

(concept) (narrower term, instance) (concept)

person NTI Roger Federer

• Associative relationship (RT): link between concepts that are not hierarchically related, but still “semantically or conceptually associated to such an extent that the link between them needs to be made explicit in the thesaurus, on the grounds that it may suggest additional or alternative [concepts]

(concept) (narrower term, instance) (concept)

6

6 As in most definitions above „term“ was replaced by „concept“. This correction is valid in the light of the provided data model of the BS 8723 Data model (2008).

for use in indexing or retrieval”. One concept “should always be

implied within the common frames of reference shared by the users of the thesaurus”, e.g.

marriage RT couple

Particularly the definition of associative relationships reveals that a thesaurus always has some external warrant influencing its development. Generally this warrant is based on the self-understanding of the domain’s community or a specific organization. In this sense a thesaurus forms a closed world and aims at explaining a defined domain exhaustively. Missing elements are considered errors or weaknesses of the thesaurus.

(concept) (related term) (concept)

5.3 Thesaurus usage The traditional purpose of a thesaurus in an information retrieval system is to ensure that information resources are indexed with the same term that a searcher will use when formulating a search query (BS 8723-2 2005, chap.5). Also the condition for a correctly applied associative relationship reveals how strongly thesaurus semantics is connected with thesaurus usage for (1) indexing and (2) information retrieval.

Thesaurus-based indexing can be seen as assigning thesaurus concepts in the form of preferred terms to specific metadata fields. Metadata is data about data. In the context of thesaurus-based systems metadata is about works that are collected in a library, document management system, database or other repositories. Works are documents, images and other intellectual or artistic products. Indexing often expresses the aboutness of such works, in a “subject” metadata field. Sometimes there are also other metadata fields that are filled with terms from a thesaurus or other types of controlled vocabularies, e.g. the isness or ofness of works (IFLA 2010). The isness often indicates a genre (e.g. short story) or other classifications (e.g. textbook, poster, CD-ROM). The ofness can indicate the situation or object that is described or displayed in a work (e.g. a sunflower, an accident). The aboutness generally expresses more abstract ideas about a work (e.g. war, happiness). Figure 4 illustrates this relatedness between concepts and works. The combination of several concepts/preferred terms describes more complex and hence more specific concepts as subject of a work.

In a similar fashion thesaurus-based information retrieval systems require the user to select (a combination of) search terms from the thesaurus to formulate a search query or for refining a search query. Alternatively free-text search queries need to be mapped to (preferred or non-preferred) terms in the thesaurus (Blocks et al. 2006). Another common way of exploiting a thesaurus in information retrieval is its use for manual, automatic or interactive search expansion (Shiri & Revie 2006).

6 Comparison of ontologies and thesauri

6.1 Definition-based comparison Based on the definitions in the British thesaurus- and W3C’s OWL- standard there are numerous elements in an ontology that have no correspondent element in a thesaurus at all: the attributes, expressions of all types, and all axioms – except for the ones described below. The

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same also accounts the other way around: thesaurus elements such as node labels for indicating facets, the distinction between simple non-preferred terms and compound non-preferred terms and the associated ‘compound equivalence’ relationship between preferred and compound non-preferred terms do not have any correspondent element in an ontology.

The clearest definition-based correspondences can be found for the generic relationship and the instance relationship of thesauri. These elements correspond to the sub-class axiom and the class assertion in ontologies respectively (see table 2). A practical problem with this correspondence is that thesauri do not have to distinguish generic, whole-part and instance relationships, but can use the general hierarchical relationship instead. This might even be the case for most existing thesauri today. A general hierarchical relationship as well as its more specialized whole-part relationship and also the associative relationship do not have any correspondent axiom or other element in an ontology.

Thesaurus Ontology Concept often: Class

sometimes: Individual Term (preferred and non-preferred term) (Custom) Label Associative relationship Hierarchical relationship

Generic relationship Subclass of axiom Instance relationship Class assertion Whole-part relationship

Note (scope note, history note, definition, editorial note) (Custom) Comment

Custom attribute (Custom) Annotation

Table 2: Correspondence of thesaurus and ontology elements based on their definitions

The possibility to match generic and instance relationships in a thesaurus in the described way combined with the fact that the subclass axiom and the class assertion connect classes and individuals (see figure 3) lead to the conclusion that some thesaurus concepts have to be considered ontology classes whilst others need to be treated as individuals in ontologies.

Thesaurus terms in general match the role that labels (as types of annotations) have in ontologies. Nevertheless, ontologies do not provide possibilities to distinguish between preferred terms and non-preferred terms. A custom extension of labels would be the most approach for integrating this thesaurus knowledge.

The same basically accounts for thesaurus notes, which rather match the role of comments in ontologies. Again, ontologies do not provide any appropriate subtypes of annotations for scope notes, history notes, definitions or editorial notes in specific. The custom definition of subtypes of comments would be the most sensible approach again. The definition of custom annotations is also the way in which other custom thesaurus attributes can be transferred to ontologies.

6.2 Usage comparison For comparing the usage of thesauri and ontologies it is expedient to consider the entire process chain of developing thesauri and ontologies until their final usage.

Table 3 distinguishes three steps for thesauri and ontologies each. The way they are aligned horizontally reveals some approximate similarity of the activities that will be subject of forthcoming discussion.

Ontology Thesaurus Specifying vocabulary Developing thesaurus

(a type of controlled vocabulary) Making assertions Indexing/ filling metadata fields

Reasoning Information retrieval

Table 3: Contrasted activities of constructing and using ontologies and thesauri

The ontology activities of specifying a vocabulary and making assertions correspond to the two metalevels “domain vocabulary” and “domain objects” that have been introduced to explain the design of an ontology in section 4.2 (table 1). Specifying a vocabulary in an ontology can be compared with developing the whole of a thesaurus. Making assertions in an ontology has similarity to the indexing activity that has been described as use case for thesauri. Nevertheless, both activities are not the same. As expressed earlier indexing is expressing the aboutness, isness or ofness of works (see figure 4). In contrast, asserting in an ontology means making a statement about a real-life object, e.g. about someone’s family relation or the health condition of a specific patient.

Ontology Thesaurus

Class Class Concept Concept Concept

Individual Individual Work Work attribute attribute

Figure 4: Expressivity of ontologies and thesauri about things (individuals vs. works)

In some cases a class assertion may be comparable to the expression of the isness of a work when indexing with a thesaurus. There are no correspondent notions for the aboutness and ofness in an ontology, though. Instead, using assertions and the vocabulary that has been specified through axioms and expressions, an ontology allows relating real-life objects (individuals) through object properties or describing attributes (data properties) of these real-life objects (see figure 4). From this perspective ontologies and thesauri have different foci of what things they can describe and what they can express about these things. The distinction of real-life objects and works can be challenging at times and become subject of philosophical discussions. For example unique items in a museum or the people described in a company’s expert finder7

The means-to-an-end usage of ontologies that was described in section

are physical objects of real life. Nevertheless, they can be perfectly described using a thesaurus and rather have the role of a work in these systems. Notably, making assertions in an ontology is considered part of the ontology while indexing is considered a thesaurus usage.

4.3 is reasoning about the described

7 An expert finder – sometimes also called corporate Yellow Pages – refers to a knowledge management system here.

assertion assertion

aboutness ofness isness

relation

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knowledge. The pendant for a thesaurus is its usage for information retrieval. If a thesaurus is used for automatic search expansion, the applied algorithms exploit the thesaurus relationships in a somewhat comparable, but certainly simpler manner than algorithms for (automatic), logic-based reasoning about ontologies. In contrast to ontologies, use cases of thesauri generally involve humans, e.g. in indexing, selecting a search term or when refining search queries.

6.3 Semantic comparison While there is obviously a match of definitions and some form of comparability of the uses of thesauri and ontologies, there is finally the question to what extend there is a correspondence of what the respective elements actually represent. Individuals as they are presented in the OWL standard refer to objects in reality. Intellectual or artistic works that are described with thesauri are not such objects of reality. They can only be the basis for producing specific physical items, e.g. a specific printed book, a specific print copy of an image or a specific copy of a file on the computer.

Classes represent collections of individuals, but concepts are not collections of works. Concepts are ideas that exist in the mind of humans. In a semantic sense there is no correspondence between thesauri and ontologies at all. The correspondence is reduced to what humans associate with the label of an ontology entity on the one hand and the terms of thesaurus concepts on the other hand. Nevertheless, this does not belong to the semantics that an ontology captures.

From a linguistic perspective thesauri and ontologies represent different approaches to modelling meaning, i.e. relationships between language, thought and reality. A thesaurus must be regarded as an approach, which ignores philosophical and psychological consideration of meaning and thought and concentrates on sense relations within a (natural) language, or between languages. Such approach would be “characteristic of traditional semantics and especially lexical semantics, with its concentration on semantic relationships like ambiguity, synonymy, and so on.” (Saeed 2009, p.47). Such focus is inherent to thesauri as controlled vocabularies. The relationships in a thesaurus are simply to support their navigation. Ontologies in contrast are typical for treating meaning as denotation. They are “beefing up denotational theories to cope with referential characteristics of different linguistic categories and the problems of mental entities” (Saeed 2009, p.47).

Further, the open-world assumption of ontologies is important to contrast to the closed-world build through a thesaurus. Isolated parts of ontologies are valid statements. Ontologies are supposed to be combined with each other in order to agglomerate all available knowledge and to come about new conclusions from this knowledge through reasoning algorithms. Isolated parts of thesauri make relatively little sense by themselves. Thesauri provide a holistic viewpoint on a clearly enclosed domain. Principally, there are other viewpoints possible and one viewpoint has to be seen entirely in order to make sense.

7 Implications from the comparison

7.1 Relation between thesauri and ontologies The presented comparison has implications for common perceptions of ontologies and thesauri, one of which is that ontologies and thesauri are types of vocabularies (Hodge 2009, pp.6-7; Broughton et al. 2005; BS 8723-3 2007). A (controlled/structured) vocabulary is a “set of terms, headings or concept codes and their inter-relationships” (BS 8723-1 2005, sec.2.33). Vocabularies are also associated with the term knowledge organization (KO) – schemes for “organizing information and promoting knowledge management” (Hodge 2009, p.3).

While there is no doubt about a thesaurus being a controlled/structured vocabulary, this must be questioned for ontologies. Vocabularies such as thesauri organize a domain by concepts. Their focus on terms is basically their semantics. The labels and other annotations found in ontologies are not only optional, but there is also a lack of rules and guidelines on how to use them. This may not surprise since they are not part of an ontology’s semantics. Also the IRI of an entity is not useful as a human-readable label. It functions as an identifier.

Other publications treat thesauri as a type of ontology – generally as “lightweight ontologies” (Giunchiglia & Zaihrayeu 2009). Such explicit depiction of thesauri as ontologies is rare. More often implicit treatments of thesauri as ontologies can be found. For example, G. G. Chowdhury & S. Chowdhury (2007) provide examples of ontologies, which are actually vocabularies: UMLS, a set of “terminology, classification and coding standards, and associated resources”8 or the Gene Ontology – a “controlled vocabulary, a set of standard terms – words and phrases, used for indexing and retrieving information [... and defining] relationships between the terms, making it a structured vocabulary”9

The comparison in this paper supports the rejection. The structure in thesauri is not one that is useful for reasoning tasks. While thesaurus-based systems certainly provide functionality that allows making use of the thesaurus relations, these algorithms cannot be regarded as logic-based inference. Simply re-labeling vocabularies as lightweight ontologies does neither provide any benefit to the scientific community nor to practitioners in industry. It only leads to some undesired effects, for which the case in the

. G. G. Chowdhury & S. Chowdhury also claim that browsing, searching and sense disambiguation are applications of ontologies and thus make ontologies appear to be types of vocabularies. Similar examples can be found in the “Handbook of Ontologies” where Robert Stevens & Lord (2009, p.741) find that “the single most common use of ontology in bioinformatics is to provide a controlled vocabulary, which is then used to provide annotation for database entries”. This directly contradicts the article by Guarino et al. (2009) in the very same handbook of ontologies, who provide a minute definition of ontologies and an explicit rejection of considering thesauri and other vocabularies as ontologies.

introduction was an example:

8 http://www.nlm.nih.gov/research/umls/ 9 http://www.geneontology.org/GO.ontology.structure.shtml

42

• Relevant thesaurus and vocabulary literature is not found. The application of existing knowledge about thesauri and building up on respective research is impeded. Hence, there is the danger of repeating mistakes and reinventing the wheel.

• Ontology literature is used in scenarios that it not applicable and was never intended for.

• It is made difficult to declare the scope of research results or the nature of domain models when “everything” is treated as an ontology.

The same effects must be expected when treating ontologies as types of vocabularies.

7.2 Remark on the role of SKOS SKOS, which has been briefly mentioned in section 2, describes itself as a “standard, low-cost migration path for porting existing knowledge organization systems to the Semantic Web”. Generally ontologies are associated with the Semantic Web. The question rises, what role SKOS fills. This shall be briefly clarified in this sections in the light of how thesauri and ontologies have been contrasted.

From the perspective of OWL SKOS is a formally specified vocabulary, i.e. an instance of its model structure. SKOS as such a vocabulary is able to describe concepts and their relatedness in a given domain in a thesaurus-like manner. If one sees ‘ontologies’ to be ultimately concerned with the description of individuals, then SKOS is about concepts of a domain while ontologies would be stereotypically about real-life objects in that domain. If one associates the word ‘ontology’ rather with the formal specification of a vocabulary, then SKOS is an ontology about the domain “general thesaurus structure”, not about a domain in the sense of a thesaurus’ content, i.e. its subject field.

Whether this is considered a contribution to the Semantic Web depends on one’s intention. If the expectation is reasoning about thesaurus structures, i.e. checking the consistency of a domain-specific thesaurus (e.g. whether there are hierarchical loops specified that contradict the thesaurus specification) or checking whether thesauri can be integrated, then publishing a thesaurus in the SKOS format is a decent choice. If the intention is contributing knowledge of a thesaurus’ subject field to the Semantic Web, then SKOS cannot help. Instead, a thesaurus would have to be re-engineered to an ontology, which generally means building an ontology from scratch, possibly using some thesaurus concepts as input. It is also not possible to reason about anything indexed with the concepts of a domain-specific SKOS vocabulary, since indexing connections are informal from an ontology perspective. SKOS should be primarily regarded as a publication format for thesauri on the Internet.

8 Conclusions and future activities This paper described and contrasted thesauri and ontologies from a semiotic perspective. The anaylsis revealed that thesauri and ontologies have significant differences. Based on the definition of elements in thesauri and ontologies there are only some refined hierarchical relationships of thesauri that can be matched

to axioms in ontologies. From a semantic perspective there is basically no match between thesauri and ontologies. The labels that can be optionally attached to entities in ontologies have a different function than the terms in a thesaurus. Also the purpose for which thesauri and ontologies are entirely different: thesauri are rather focused on the terminology of human language, support navigating through these terms to finally index works and to search for them; OWL-based ontologies are designed to describe objects of reality and to ultimately reason over the knowledge described about these objects.

The findings contradict the treatment of ontologies as types of (controlled/structured) vocabularies and vice versa. At this point it could just be speculated what reasons drove and drive this development. Regardless of the reasons, today’s situation causes practitioners and researchers spending considerable time in finding a path through the wealth of literature, recognizing the existence of thesauri besides ontologies and vice versa, differentiating them from each other and from further models as well as understanding their nature and usefulness. This may be dependent on chance events as described in the introduction and can take months, if not even years. Practices that reinforce such developments should be actively challenged.

The described distinction of thesauri and ontologies may not yet allow determining unambiguously, if a model found in practice is a thesaurus, an OWL-conformant ontology or neither of them. Such endeavours require the definition of qualitative criteria for thesauri and ontologies. Nevertheless, the depicted discrimination between thesauri and ontologies can serve as a discussion basis and may find entrance to the standardization process of part 2 of the ISO standard 25964. A standardization process is naturally a process of gaining consensus. Nevertheless, the result finally also imposes a certain usage of the terms ontology and thesaurus.

The success of standardization efforts depends on the bandwidth of involved people. ISO standardization processes are neither public nor is it free of costs to participate in them. Since even the finally produced standards are not free of costs, the effectiveness of the standardization effort will be inevitably limited. Alternatives include the publication of results as articles on Wikipedia or other publically available encyclopaedias. This would at least influence the “public” opinion of what is a thesaurus as opposed to an ontology.

9 References Aitchison, J., Gilchrist, A. & Bawden, D., 2000.

Thesaurus construction and use: a practical manual 4th ed., Aslib London.

ANSI/NISO Z39.19, 2005. Guidelines for the Construction, Format, and Management of Monolingual Controlled Vocabularies.

Antoniou, G. & van Harmelen, F.V., 2009. Web Ontology Language: OWL. In Handbook on Ontologies. pp. 91-110.

Beck, H. & Pinto, H.S., 2003. Overview of Approach, Methodologies, Standards, and Tools for Ontologies.

Bennett, S. & Skelton, J., 2001. Schaum's Outline of UML 1st ed., McGraw-Hill.

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Blocks, D., Cunliffe, D. & Tudhope, D., 2006. A reference model for user-system interaction in thesaurus-based searching. Journal of the American Society for Information Science and Technology, 57(12), pp.1655-1665.

Broughton, V. et al., 2005. Knowledge Organization. In European curriculum reflections on library and information science education. The Royal School of Library and Information Science, pp. 133-148.

BS 8723, 2005. Structured vocabularies for information retrieval. Guide,

BS 8723 Data model, 2008. BS 8723 Data model. Available at: http://schemas.bs8723.org/Model.aspx.

BS 8723-1, 2005. Definitions, symbols and abbreviations. In BS 8723: Structured vocabularies for information retrieval. Guide. British Standards Institution (BSI).

BS 8723-2, 2005. Thesauri. In BS 8723: Structured vocabularies for information retrieval. Guide. British Standards Institution (BSI).

BS 8723-3, 2007. Vocabularies other than thesauri. In BS 8723: Structured vocabularies for information retrieval. Guide. British Standards Institution (BSI).

BS DD 8723-5, 2008. Exchange formats and protocols for interoperability. In BS 8723: Structured vocabularies for information retrieval. Guide. British Standards Institution,Committee IDT/2/2.

Chowdhury, G.G. & Chowdhury, S., 2007. Organizing information: from the shelf to the web, London, UK: Facet Publishing.

Fernández-López, M. & Gómez-Pérez, A., 2003. Overview and analysis of methodologies for building ontologies. The Knowledge Engineering Review, 17(02), pp.129-156.

Fischer, D.H., 1998. From Thesauri towards Ontologies? In Proceedings of the fifth International ISKO Conference, 25-29 August 1998. Structures and relations in knowledge organization. Lille, France: Ergon Verlag, p. 18.

Garshol, L.M., 2004. Metadata? Thesauri? Taxonomies? Topic Maps! - Making sense of it all. Journal of Information Science, 30(4), pp.378-391.

Génova, G., Llorens, J. & Martínez, P., 2002. The meaning of multiplicity of n-ary associations in UML. Software and Systems Modeling, 1(2), pp.86-97.

Gilchrist, A., 2003. Thesauri, taxonomies and ontologies – an etymological note. Journal of Documentation, 59(1), pp.7 - 18.

Giunchiglia, F. & Zaihrayeu, I., 2009. Lightweight Ontologies. In Encyclopedia of Database Systems. Springer-Verlag.

Guarino, N., Oberle, D. & Staab, S., 2009. What is an Ontology? In S. Staab & R. Studer, eds. Handbook on Ontologies. International Handbooks on Information Systems. Springer, pp. 1-17.

Hartmann, J. et al., 2005. Methods for ontology evaluation, Karlsruhe: University of Karlsruhe.

Hodge, G., 2009. Systems of Knowledge Organization for Digital Libraries: Beyond Traditional Authority Files,

Washington: The Digital Library Federation. Council on Library and Information Resources.

IFLA, 2010. Functional Requirements for Subject Authority Data (FRSAD). A conceptual model M. L. Zeng, M. Žumer, & A. Salaba, eds., Int. Federation of Library Associations and Institutions (IFLA).

ISO 2788, 1986. Documentation - Guidelines for the establishment and development of monolingual thesauri,

ISO 5964, 1985. Documentation - Guidelines for the establishment and development of multilingual thesauri,

OMG ODM, 2009. Ontology Definition Metamodel v1.0 1st ed., Object Management Group (OMG).

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Sabou, M., 2007. Methods for Selection and Integration of Reusable Components from Formal or Informal User Specifications, Open University (OU).

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within a thesaurus-enhanced search environment: A user-centered evaluation. Journal of the American Society for Information Science and Technology, 57(4), pp.462-478.

Soualmia, L.F., Golbreich, C. & Darmoni, S.J., 2004. Representing the MeSH in OWL: Towards a semiautomatic migration. In Proceedings of the KR 2004 Workshop on Formal Biomedical Knowledge Representation. pp. 81-87.

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Uschold, M. & Grüninger, M., 2004. Ontologies and semantics for seamless connectivity. ACM SIGMOD Record, 33(4), pp.58-64.

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W3C OWL 2 Primer, 2009. OWL 2 Web Ontology Language. Primer.

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W3C SKOS, 2009. Simple Knowledge Organization System Reference, World Wide Web Consortium (W3C).

Wroe, C.J. et al., 2003. A methodology to migrate the Gene ontology to a description logic environment using DAML OIL. In Proceedings of the 8th Pacific Symposium on Biocomputing (PSB). Hawaii, pp. 624--635.

44

Fast Classification in Protege:Snorocket as an OWL 2 EL Reasoner

Michael J. Lawley1 Cyril Bousquet2

1The Australian e-Health Research CentreICT Centre, CSIRO

Brisbane, QueenslandEmail: michael.lawley@csiro.au

2 Universite Technologique de Belfort-MontbeliardMontbeliard, France

Email: cyril.bousquet@utbm.fr

Abstract

Snorocket is a high-performance implementation ofthe polynomial-time classification algorithm for thelightweight DL EL++. Until recently it has only beengenerally available in a form suitable for classifyingthe biomedical ontology Snomed ct. To make thiscross-platform reasoner more generally available tothe DL community, Snorocket now implements theOWL API and is thus available1 as a Protege plu-gin. Additionally, through the use of OWL Anno-tations we have enabled support for the partial in-cremental classification functionality of Snorocket inorder to greatly ease the use of Protege for manipulat-ing very large ontologies. Benchmarking results arepresented for both full and incremental classificationdemonstrating that Snorocket is the only reasoner ca-pable of handling all the test ontologies at the time oftesting, and is at least an order of magnitude fasterthan the fastest other Protege reasoner tested.

1 Introduction

The development of a new polynomial-time algo-rithm Baader et al. (2006) for the lightweight descrip-tion logics in the EL family has been a significant re-cent advance, leading to the first academic DL systemcapable of classifying the very large clinical ontologySnomed ct. Subsequently, there has been a renewedinterest in classifiers capable of working with a rangeof biomedical ontologies that exhibit particular struc-ture amenable to specific optimisations.

However, the algorithms implementation in CEL2

faces several barriers to wider use, not least of which isthe limitation to Linux-based operating systems only.

This paper describes and presents performancemeasures for Snorocket, another implementation ofthe algorithm, this time in Java, which is cross-platform, is at least an order of magnitude fasterthan CEL, has been licensed by the InternationalHealth Terminology Standards Development Organi-sation (IHTSDO) for use in their Snomed ct Work-bench, and has recently been adapted as a Protege

Copyright c©2010, Australian Computer Society, Inc. This pa-per appeared at the Sixth Australasian Ontology Workshop(AOW 2010), Adelaide, Australia. Conferences in Researchand Practice in Information Technology (CRPIT), Vol. 122,Thomas Meyer and Mehmet A. Orgun and Kerry Taylor, Ed.Reproduction for academic, not-for-profit purposes permittedprovided this text is included.

1http://research.ict.csiro.au/software/snorocket2http://cel.googlecode.com/

plugin including support for (partial) incrementalclassification.

2 Background

The initial motivation for Snorocket was the desirefor a classifier that could process extended versionsof Snomed ct Lawley (2008). The major problemwith existing classifiers was one of scale. The July2009 international release of Snomed ct consists ofapproximately 310,000 active Classes, 63 Properties,and 370,000 axioms, until quite recently beyond thecapabilities of most reasoners (e.g., FaCT++ and Rac-erPro). A second issue is that Snomed ct is not rep-resented directly in a standard description logic form,but uses its own representation that comprises:

• a concepts file identifying each of the Classes andProperties, and whether a Class is primitive ornot,

• a relationships file describing SubClassOf andObjectSomeValuesFrom expressions, and

• a descriptions file detailing the labels and syn-onyms.

Snomed ct also includes a mechanism known as rolegrouping Spackman et al. (2002) that, although itcan be transformed away to produce a correspond-ing description logic representation, requires specialhandling when interpreting classification results.

Prior to the January 2009 International Release ofSnomed ct, its stated form was only made availableon a limited basis for academic research, along withan unofficial Perl script to transform it into to eithera KRSS or OWL/XML representation. Possibly be-cause of this, many publications use older, out-of-dateversions of Snomed ct rather than the most recentlyavailable one. However, the stated form and the Perlscript are now part of the official standard release andare thus much more easily accessible (usually from anational release centre).

With the recent adoption of the OWL 2 Web On-tology Language (OWL2) as a W3C Recommenda-tion W3C (2009b), there is now a standard profile,OWL2 EL W3C (2009a), that corresponds to EL+.This profile (a fragment or sub-language of OWL2) issummarised in Table 1.

It is a relatively simple exercise to update theaforementioned Perl script to produce an OWL2Functional Syntax representation of Snomed ct thatconforms to this profile. The result can then beloaded, albeit slowly, into tools such as Protege.

45

Table 1: Constructs in the OWL2 EL Profile, Snorocket supported constructs in bold.

Thing NothingObjectSomeValuesFrom DataSomeValuesFromObjectIntersectionOf DataIntersectionOfSubClassOf EquivalentClassesDisjointClassesSubObjectPropertyOf SubDataPropertyOfEquivalentObjectProperties EquivalentDataPropertiesTransitiveObjectProperty ReflexiveObjectPropertyObjectHasValue DataHasValueObjectHasSelf ClassAssertionObjectOneOf DataOneOfObjectPropertyDomain DataPropertyDomainObjectPropertyRange DataPropertyRangeSameIndividual DifferentIndividualsObjectPropertyAssertion DataPropertyAssertionNegativeObjectPropertyAssertion NegativeDataPropertyAssertionFunctionalDataProperty HasKey

3 Snorocket implementation

While Snorocket was originally implemented asa cross-platform classifier specifically targeted atSnomed ct, the developments detailed in the pre-vious section have motivated the development of aProtege plugin form of Snorocket. Note that, at thistime, Snorocket does not support individuals or do-main and range constraints; the supported constructsare in bold face in Table 1.

The implementation of Snorocket is organised intoseveral components:

au.csiro.snorocket.coreContains the core algorithm implementation in-cluding support for incremental classification ofadditions only.

au.csiro.snorocket.snapiContains the significant extra code to deal withSnomed ct-specific functionality including:

• pre- and post-processing of role group-ing Spackman et al. (2002), IHTSDO (2009)including incremental classification sup-port,

• Snomed ct-specific constants and meta-data, and

• post-processing routines to generate theSnomed ct distribution-format results.

It has a well-defined Java API modelled aroundthe Snomed ct standard distribution file for-mats.

au.csiro.snorocketContains the command-line wrapper to drive theclassifier along with parsers for various input fileformats: two variants of KRSS, the Snomed ctdistribution format, and OWL2 Functional Syn-tax W3C (2009b).

au.csiro.snorocket.aceContains a thin wrapper around the moduleau.csiro.snorocket.snapi to interface to theIHTSDO Workbench.

au.csiro.snorocket.protegeContains an implementation of the OWL APIclass OWLReasoner that wraps the core im-plementation, au.csiro.snorocket.core, andconverts from the OWL API representation ofaxioms to that of Snorocket.

3.1 Experimental results with Protege rea-soners

A set of experiments were performed on a computerequipped with a 3 GHz Intel R© Core 2 Duo proces-sor, 4 GB of physical memory, and running UbuntuLinux. Protege was run with Java 6 and a maxi-mum heap size of 1900 MB3. All the experiments de-scribed in this part use the CPU time as an indicator.To achieve comparable measurement, external timinghas been used to check the validity of the results.

The four Protege reasoners tested were Fact++,Pellet, CEL and Snorocket. These plugins vary in thesense that they have been implemented using differentalgorithms and different technologies. The core ofFact++ is implemented in C++, Pellet and Snorocketin Java, and the core of CEL in Common Lisp.

The set of ontologies4 chosen for testing allcome from the life sciences domain, and havebeen used in other performance comparisons Sun-tisrivaraporn (2008a), Mendez & Suntisrivaraporn(2009). They include the Gene Ontology (Go);a large classification ontology from the US Na-tional Cancer Institute (Nci); the FoundationalModel of Anatomy (Fma)5; two versions of theGalen medical knowledge base (Galen)6; and theSystematized Nomenclature of Medicine, ClinicalTerms (Snomed ct). In addition, we have includedboth the original stated form of Snomed ct as wellas the distribution form which is derived from theinferred form; the axioms specify all inferred Proper-ties but only immediate parent Classes. Table 2 givessome details of these ontologies. For more backgroundon these ontologies see Suntisrivaraporn (2008a).

For each ontology we ran the reasoners five timesand threw away the longest time (in most cases, thiswas from the initial run) before computing an averagetime. These averages are displayed in Table 3. If thereasoner failed due to an out-of-memory exception, itis indicated by o/m, and if it crashed it is indicatedby exit.

These results show clearly how much fasterSnorocket is, especially for the larger ontologies where

3The maximum heap we could allocate using a 32bit JVM4Most are available at: http://lat.inf.tu-dresden.de/~meng/

ontologies/5This is a different version to that used in Suntisrivara-

porn (2008a), Mendez & Suntisrivaraporn (2009) and is avail-able from http://www.bioontology.org/projects/ontologies/fma/fmaOwlFullComponent_2_0.owl

6Property inverses and functionalities were excluded fromGalen.

46

Table 2: Profiles of the various test ontologies.

#Classes #Properties #AxiomsOntology PCDef CDef GCI RIGo 26270 6 63426 0 0 0Nci 27652 70 46800 0 0 0Fma 78990 113 82343 0 0 0NotGalen 2748 413 3238 699 357 416FullGalen 23141 950 25563 9968 1951 957Snomed ct (stated) 386965 63 443725 59182 0 11Snomed ct (dist.) 386965 63 595182 59182 0 11

Table 3: Average classification times using various reasoners in Protege on Linux.

Go Nci Fma NotGalen FullGalen Snomed ct Snomed ct(stated) (distribution)

FACT++ 7.69 3.82 exit 2.78 o/m 597 1287Pellet 1.54 5.68 o/m 1.20 100 o/m o/mCEL 1.07 2.53 o/m 2.26 141 760 o/mSnorocket 0.06 0.19 2.68 0.15 6.37 58.3 54.8

the order of magnitude speed difference is especiallyapparent to the user (six seconds vs more than oneminute for FullGalen, and one minute vs more thanten minutes for Snomed ct).

4 Incremental classification

For the special case of additions (only) to an ontol-ogy that has already been classified, it is possibleto re-use the previously computed classification in-formation and to compute the newly inferable rela-tionships Suntisrivaraporn (2008b). This functional-ity is especially useful for very large ontologies suchas Snomed ct. The Snorocket core implementationsupports this kind of incremental classification andis also able to save and later restore its state afterclassifying an ontology.

Through the use of specific Annotations to an on-tology, the Snorocket plugin for Protege is able to re-store a previous state and then perform partial incre-mental classification. This provides a usable environ-ment for either building extensions to large ontologiessuch as Snomed ct or editing pre-selected fragmentsafter first partitioning the ontology into a large fixedset of axioms and a smaller changeable set.

To do this, one would classify the fixed ontologytag:fixed.owl and store it in a file file:base.txt.This only needs to be done once. The editable on-tology tag:editable.owl would then import tag:fixed.owl and include two annotations, one indi-cating the URI of the pre-classified ontology (tag:fixed.owl), and the second indicating the locationof the state file (file:base.txt). Figure 2 illustratesan example extension of a subset of Snomed ct.

This information is then used by the SnorocketOWL API reasoner to determine where to load thepre-computed state from, and which set of axioms itdoes not need to process (because they are alreadyrepresented in the restored state).

Note, because of the Import(<...>) clause,Protege will still load the (large) set of axioms in thereferenced ontology even though Snorocket does notneed to. To avoid Protege slowing down due to ex-cessive RAM usage, it is possible to omit this clause

Table 4: Incremental classification times

#Additional Timeaxioms (seconds)

2 0.810 0.930 1.250 1.1

100 1.2200 2.0400 2.2800 5.8

1000 7.02000 10.84000 20.0

without affecting the behaviour of Snorocket becausethe pre-computed state already contains sufficient in-formation in in a much more compact representation.

4.1 Experimental results for incrementalclassification

We performed two separate evaluations of incremen-tal classification times for Snorocket. First, we createda fixed subset of Snomed ct consisting of 351261concepts and an approximately equal number of ax-ioms. We then measured the time it took to incre-mentally classify some number of additional axioms.The results are given in Table 4. Note that thesefigures do not include the time taken to load the pre-computed state (approximately 12 seconds) since thisis only necessary for the very first classification.

In the second evaluation we used the same fixedsubset of Snomed ct and five different sets of addi-tional axioms of roughly the same size. The resultsindicate that the incremental classification time is es-sentially stable for a reasonably sized addition of ax-ioms.

47

Figure 1: Performance comparison

Namespace(owl=<http://www.w3.org/2002/07/owl#> )Namespace(owl2annotation=<http://aehrc.com/snorocket/owl2annotation#>)Namespace(=<http://www.ihtsdo.org/> )Namespace(base=<http://www.ihtsdo.org/> )

Ontology(<http://www.ihtsdo.org/SCT7>Annotation(owl2annotation:BaseUri "http://www.aehrc.com/ontologies/A.owl")Annotation(owl2annotation:BaseState "file:A.owlSnorocketProtegeState.txt")

Import(<http://www.aehrc.com/ontologies/A.owl>)

EquivalentClasses( SCT_162957009ObjectIntersectionOf(

SCT_366136002SCT_272016000ObjectSomeValuesFrom( RoleGroup ObjectSomeValuesFrom( SCT_363698007 SCT_51185008))ObjectSomeValuesFrom( RoleGroup ObjectSomeValuesFrom( SCT_363698007 SCT_82094008))ObjectSomeValuesFrom( RoleGroup ObjectSomeValuesFrom( SCT_418775008 SCT_37931006))ObjectSomeValuesFrom( RoleGroup ObjectSomeValuesFrom( SCT_419066007 SCT_420158005))ObjectSomeValuesFrom( RoleGroup ObjectSomeValuesFrom( SCT_363714003 SCT_79466001))

))

)

Figure 2: Example annotated extension of a Snomed ct subset.

5 Concluding remarks

The experimental results from the previous section inconjunction with comparable results in benchmarkingother Protege reasoners clearly show that Snorocketoffers the best performance for OWL2 EL ontologies.

The size of ontologies such as Snomed ct stillpresent performance problems for editing tools suchas Protege since they load slowly, consume largeamounts of RAM leading to sluggish behaviour, andstill take a significant amount of time to classify. How-ever, exploiting the incremental classification capa-bilities of Snorocket the classification time can be re-duced to a more acceptable level.

A further advantage is that, by omitting the Im-port statement for the ontology containing the fixedaxioms, one can avoid Protege loading the fixed ax-ioms, yet the concepts contained therein and the in-ferred relationships will be displayed in Protege afterclassification, but only in a lazy, on-demand manner,thus alleviating the slow load time and excessive RAMconsumption.

References

Baader, F., Lutz, C. & Suntisrivaraporn, B. (2006),CEL—a polynomial-time reasoner for life scienceontologies, in U. Furbach & N. Shankar, eds, ‘Pro-

ceedings of the 3rd International Joint Conferenceon Automated Reasoning (IJCAR’06)’, Vol. 4130of Lecture Notes in Artificial Intelligence, Springer-Verlag, pp. 287–291.

IHTSDO (2009), SNOMED Clinical Terms R© Tech-nical Reference Guide, International Health Termi-nology Standards Development Organisation.

Lawley, M. (2008), Exploiting fast classification ofSNOMED CT for query and integration of healthdata, in ‘KR-MED’, Vol. 410 of CEUR WorkshopProceedings, CEUR-WS.org.

Mendez, J. & Suntisrivaraporn, B. (2009), Reintro-ducing CEL as an OWL 2 EL Reasoner, in B. Grau,I. Horrocks, B. Motik & U. Sattler, eds, ‘Proceed-ings of the 22nd International Workshop on De-scription Logics (DL 2009)’, Vol. 477 of CEURWorkshop Proceedings.

Spackman, K., Dionne, R., Mays, E. & Weis, J.(2002), Role grouping as an extension to the de-scription logic of Ontylog, motivated by conceptmodeling in SNOMED, in ‘Proceedings AMIASymposium’, Vol. 712.

Suntisrivaraporn, B. (2008a), Empirical evaluation ofreasoning in lightweight DLs on life science ontolo-gies, in ‘Proceedings of the 2nd Mahasarakham In-ternational Workshop on AI (MIWAI’08)’.

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Figure 3: Incremental classification times for additional axioms

Table 5: Incremental classification times for different extensions

#Classes #Axioms Time

PCDef CDef (seconds)A1 171 103 16 3.2A2 212 187 20 2.3A3 203 150 29 3.3A4 210 154 23 1.7A5 219 110 27 1.8

Suntisrivaraporn, B. (2008b), Module extraction andincremental classification: A pragmatic approachfor EL+ ontologies, in S. Bechhofer, M. Hauswirth,J. Hoffmann & M. Koubarakis, eds, ‘Proceedingsof the 5th European Semantic Web Conference(ESWC’08)’, Vol. 5021/2008 of Lecture Notes inComputer Science, Springer-Verlag, pp. 230–244.

W3C (2009a), OWL 2 Web Ontology Language: Pro-files, World Wide Web Consortium. http://www.w3.org/TR/owl2-profiles/.

W3C (2009b), OWL 2 Web Ontology Language:Structural Specification and Functional-Style Syn-tax, World Wide Web Consortium. http://www.w3.org/TR/owl2-syntax/.

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50

Ontological Support for Consistency Checking of Engineering

Design Workflows

Franz Maier, Wolfgang Mayer and Markus Stumptner

Advanced Computing Research Centre,University of South Australia,

Mawson Lakes Campus, Mawson Lakes Boulevard,Mawson Lakes, SA 5095,

Email: franz.maier|wolfgang.mayer|mst@cs.unisa.edu.au

Abstract

In this paper we describe a novel approach for engi-neering process representation based on the applica-tion of formal ontologies. We illustrate componentsof a framework that comprises domain abstractions,design interfaces and meta-data in the engineering de-sign domain in the form of process-, artefact- andtask ontologies. A concrete application and use caseof the framework components is detailed in order todemonstrate the capabilities for representation of de-sign processes on a high level of abstraction. Therealm of Planning is employed to showcase workflowdecomposition. We show, how the framework can beapplied to perform workflow consistency checking andpoint out some scenarios where the developed frame-work can provide support in the task of engineeringdesign analysis and improvement.

Keywords: process ontology, engineering design, pro-cess integration, planning, process modelling and de-composition, consistency checking.

1 Introduction

Data and processes in engineering design environ-ments need to be formalised in an unambiguousway. High level design interfaces and design meta-data are not sufficiently integrated in the daily rou-tine of execution and composition of design work-flows (Maier et al., 2008). Ontologies of design knowl-edge are already part of manufacturing environmentswith examples being ontology supported checking ofconsistency requirements of design aspects (Tudo-rache, 2008), capturing of design rationales (Burge,2006), feature-based process planning (Jiang and Liu,2008) and manufacturing planning (Borgo and Leitao,2007). Further, ontologies can be applied to repre-sent an intermediate language between engineeringapplications, comprising applications for product life-cycle management (Fenves et al., 2003), enterpriseresource planning systems (Borgo and Leitao, 2007)and computer-aided design (Andersen and Vasilakis,2007).

The major contribution of this paper is the demon-stration of a use case that details how the introducedontology framework can be used to support workflowconsistency checking. As a means of process decom-position we will introduce a tool from the planning

Copyright c©2010, Australian Computer Society, Inc. This pa-per appeared at the Sixth Australasian Ontology WorkshopAOW 2010), Adelaide, Australia. Conferences in Researchand Practice in Information Technology (CRPIT), Vol. 122,Thomas Meyer and Mehmet A. Orgun and Kerry Taylor, Ed.Reproduction for academic, not-for-profit purposes permittedprovided this text is included.

realm that allows us to perform a refinement andgrounding of abstract engineering processes. The usecase also shows how historic process execution tracescan be utilised to construct new design scenarios. Thepaper is structured in the following way: first we in-troduce the general architecture of the framework andbriefly comment on the role of each framework layer.Then we explain in detail how each of the frameworkcomponents have been realised and how layers arelinked with each other and comment on the realisa-tion of data- and control- flow. A grounding of theprocess model will be provided and it is illustratedhow existing engineering ontologies can be utilised bythe framework. In the second part of the paper wedemonstrate the application of the framework con-cepts in the planning domain and introduce detailsof our model. Finally, a use case is introduced thatillustrates how workflow consistency checking is sup-ported by the framework.

1.1 Research Context

The integration approach was developed in the con-text of Multidisciplinary Design Optimisation (MDO)in an automotive design environment. In MDO, adesign engineer analyses all investigated design disci-plines in parallel, instead of optimising each domainseparately. The results of this process are prioritisedwith the intent to obtain the best design alternativeas a compromise of all included disciplines. As an ex-ample, an automotive design scenario could includedisciplines such as noise, vibration, harshness, driv-ing dynamics, fluid dynamics and structural statics ina single MDO experiment. MDO is typically carriedout after a basic design of a vehicle is constructed andwill be iteratively applied in the early stages of the ve-hicle design process. As a general context, the trendtoward increased virtualisation of the product devel-opment process has to be considered as well as therequirement to represent all artefacts of the design op-timisation process in virtual form. In the engineeringdesign context, ontologies support the semantic inter-operability between participating design disciplinesdue to the application of meta-models that connectbetween disciplines. Semantic-preserving translationsbetween design disciplines must be preserved and ab-stractions of design constraints and simulation resultsmust be mapped with each other.

1.2 Abstract Workflow Refinement

Using automated reasoning technology, process mod-els can automatically be translated into workflow en-actment models that are executed. This enables thedesigner to automatically track, store, and reasonabout process outcomes that are handled by the MDO

51

environment. Through common task and artefact on-tologies and adapters, simulation inputs and resultscan be compared and possible changes to the processmay be suggested and validated.

The conceptual representation of an MDO sce-nario allows us to create a workflow description thatcan subsequently be instantiated and executed. Be-fore such a workflow template can be provided, it isnecessary to develop a mapping between a high levelconceptual view of the MDO process and concreteparameter bindings that are part of a workflow de-scription. For instance a concept describing a partof the domain model has to be linked to concrete en-tities such as a geometry-model and meshing-modelthat can have concrete value assignments. This canbe done by assigning each abstract process step to arange of domain concepts that are valid in a givendesign state. The knowledge about value ranges isderived from past MDO scenarios that could success-fully be completed.

2 Related Work

Dartigues et al. investigate into semantic supportof computer-aided design (CAD) and computer-aidedprocess-planning (CAPP) activities. In additionto geometry-related product data, they employ afeature-based integration approach that relies on ashared ontology available in the Knowledge Inter-change Format (KIF). Domain specific ontologies aredeveloped after an analysis of participating engineer-ing applications is performed. Subsequently, mappingrules are created to link domain specific ontologies tothe shared ontology (Dartigues et al., 2007). Theirapproach focuses on semantically enhanced data ex-change between engineering applications, where on-tologies on features and feature decomposition are de-veloped, supported for instance by a constraint clas-sification mechanism and the identification of designspecific classes. In contrast to our approach, a taskontology for typical engineering activities is not partof the shared ontology and process planning activitiesare mainly associated with the manufacturing modelof an artefact.

Another related approach is based on a frameworkto negotiate ontology mediation dynamically (Kan-nengiesser and Gero, 2006), driven by a knowledgemodel rooted in the function-behaviour-structure on-tology (Gero and Kannengiesser, 2007). In contrast,our work adheres to the knowledge intensive ap-proach, where a mediating ontology is constructedmanually.

Kitamura and Mizoguchi provide a framework tosystematise functional knowledge of devices in an en-gineering context, resulting in a comprehensive de-vice ontology (Kitamura and Mizoguchi, 2004). Theframework has initially been applied to the mechan-ical domain and its utilisation is subsequently ex-panded to other application domains. It enablesknowledge sharing among engineering artefacts andensures their respective interoperability. Their majorcontribution is the provision of a functional ontologyfor devices. Although the framework only covers asubset of a complete behavioural model for engineer-ing artefacts, the dimensions that are introduced forclassification of functional knowledge can be reusedin the engineering design domain. The frameworkdoes not include task ontologies for typical engineer-ing activities, however, these can be found in earlierworks (Seta et al., 1998) of the same authors.

The Process Specification Language(PSL) (Gruninger et al., 2006) was designed as

formal ’interlingua’ that captures fundamentalconcepts of manufacturing processes in order tomediate between process representation formats suchthat the semantics of interrelated representationformalisms is preserved. We utilise PSL as a formalbasis to reason about task ontologies and execu-tion traces, but specialise the ontology to aspectsspecific to MDO. While PSL focuses on processes,standardised representations of product models suchas STEP (International Organization for Standard-ization, 1994), the Core Product Model and OpenAssembly Model (Rachuri et al., 2005) have also beenproposed as unifying ontologies. Further, extensionsof ISO 10303 (STEP) to represent analysis-drivendesign activities are the focus of current researchactivities (Maier and Stumptner, 2007). Here, weextend the approach to integrate artefact and processmodels into a unified framework.

3 Framework Architecture

For a detailed elaboration of the architecture andcomprised components, see (Maier et al., 2008). Theapproach taken adapts a layered architecture wherethe MDO meta-model is located at the top, task andartefact ontologies comprise the intermediate layer,and domain-specific ontologies form the bottom layerin the ontology hierarchy.

Concrete executable systems, such as CAD envi-ronments, optimisation tools and workflow enginesare located below the knowledge representation lay-ers. From analysis of individual domains, ontolo-gies of domain-specific concepts, properties and rela-tions are created, as well as specifications of domain-specific analysis primitives. Process execution envi-ronments, for example workflow enactment systems,are treated in the same way. As a result, a set ofdomain ontologies is obtained. Domain-independentaspects and processes are found by generalisationof domain-specific ontologies to form the intermedi-ate layer. By defining suitable ontology mappings,specific knowledge is mapped into the unified taskand artefact-specific ontologies at the intermediatelevel. Established engineering practices and processesmay also be incorporated into the MDO task ontol-ogy. Similarly, a generalised artefact ontology is con-structed from the artefact domain ontologies.

Task and artefact ontologies at the intermediatelayer must conform to the meta-models in the up-per layer. The common meta-model allows us todescribe and reason about domain-independent andtask-independent concepts, such as execution tracesand execution histories. Further, task and artefactontologies need not be expressed in the same formalframework and may need to be reconciled to obtainan inference framework that can handle mixed expres-sions.

4 Framework Utilisation

The general role of the outlined framework can besummarised in the following way:

• Ensuring interoperability of engineering tools byprovision of common terminology employed todescribe typical tasks, problem solving methodsand artefacts. The MDO meta-model can beused as interchange format for operative appli-cations.

• Enabling communication between knowledge en-gineers, design engineers and further stakehold-

52

Figure 1: Ontology Architecture

ers of the design process and represents commonterminology and language.

• When developing an application in the design en-vironment, concepts can be reused and the devel-opment activities can build on existing domainconcepts. Reasoning capabilities provided by theframework can support the extension of existingdomain concepts.

Beyond general framework roles, we defined con-crete use cases that utilise defined high level conceptsand their interrelations. In other words, the MDOmeta-model represents the basis for more specific on-tologies that are required to realise a particular appli-cation. Therefore, in the general case, we first haveto extend the MDO meta-model by the concepts re-quired for use case realisation before commencing itsimplementation.

5 Realisation of Framework Components

The structural part of the realised ontologies com-prised in the framework is presented here as UMLmodels that define high-level concepts of the MDOdomain. We also implemented some of the conceptsin Ontolingua as a shared ontology available for inte-gration of engineering design concepts. UML can beemployed for ontology development (Cranefield andPurvis, 1999) and is able to capture the concepts onthe meta-model layer. In the planning use case, ex-plained later in this paper, the MDO meta-modelsdepicted in UML support the decomposition of ab-stract tasks into executable process instances.

5.1 Domain Model

MDO domain concepts in combination with the MDOmeta model represent the core of the ontology frame-work. In what follows, we introduce concepts fromthe domain ontology as depicted in Figure 13, shownin the appendix of this paper. The most relevant con-cepts illustrated in the domain model are elaboratedbelow.

Concept artefact is the anchor for a majority ofincluded concepts. In contrast to the CPM ontology(Rachuri et al., 2005), where all aspects of a designartefact are represented, we mainly focus on func-tion and form of an artefact and do not representbehaviour and features of an artefact. The form ofan artefact represents a potential design solution in-tended as a result of a simulation scenario. This is inaccordance with existing work (Regli et al., 2009) inmodelling of the engineering design domain.

Besides the reference to its format, an arte-fact includes concepts to describe its construction

and configuration process, the former referring tothe creation of an artefact achieved for instancevia source-code, the latter addressing parametri-sation of an existing artefact. These entities,not included in the top-level of CPM, are intro-duced due to the emphasis of the process view,inherent in our process meta-model. Both con-cepts have further sub-concepts such as meshing-configuration and geometry-configuration as well astopology-construction and geometry-construction, tomake a functional distinction corresponding to a par-ticular MDO task respectively.

The tool concept includes attributes as typicalcharacteristics for manipulation of engineering mod-els. Each tool comprises a set of input and outputparameters, a set of accepted formats and documen-tation among other properties. Closer attention tothe tool aspect is given in grounding and execution ofa simulation scenario, where a realisation as workflowengine or finite element analysis application could benecessary.

In order to obtain a physical equivalent to the in-troduced abstract terms, each concept tagged withthe stereotype domain model has a Manifestationthat includes a URI—the pointer to the correspond-ing resource—as well as a Format and Revision forfurther specification. Manifestation is modelled asa trait (Schaerli et al., 2002) that represents an ab-straction of properties that are common to multipledisjoint concepts of the domain model. A trait sup-ports structuring of the conceptual model as it is avaluable means of concept reuse. The stereotype do-main model is attached to those domain concepts thatoccur as input or output of MDO processes. Domainmodel is used in the meta-model layer as a means toestablish the link between domain and process model.

Further, the concept meta-data provides addi-tional information on an artefact beyond its physi-cal realisation and in most cases is used in conjunc-tion with concept Manifestation. Attributes such ascreation-date, creator, owner, comment and documen-tation are included in the meta-data information. Inmany cases the introduced artefact concept will onlyappear in form of its constituents manifested as do-main models. All concepts mentioned have furthersub-concepts.

5.2 Linking MDO Domain Ontology Con-cepts with MDO Process Model

The MDO meta-model has its main focus on the pro-cess view of MDO. In order to cover the previouslydetailed design artefacts on the meta-model layer, ad-ditional modelling constructs are necessary.

Figure 2 shows the MDO meta-model extendedwith the domain conceptualisation, represented bythe entity DomainModel. DomainModel has beenused as a stereotype in the domain conceptualisationto label input and output parameters of processes.A DomainModel, a specialisation of entity Parame-terValue, is linked to the process model via conceptDataFlow that appears either as a source or as a tar-get of a Port. All DomainModels have a Manifes-tation assigned that points to its physical represen-tation. A ParameterValue can be associated with aConstraint in a Process that represents either pre- orpost-condition of a Process.

5.2.1 Control and data flow

Dataflow is realised in the process model via Portsthat are source or target of a DataFlow. DataFlow

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Figure 2: Extension of Process Meta-model with Do-main Entities

Figure 3: Control and Data Flow in MDO ProcessModel

represents data channels to route ParameterValues asdesign artefacts and constraints to MDO processes.The previously described DomainModel can eitherrepresent primitive values such as strings and inte-gers, or, sophisticated data as for instance an analysis-model or an assembly-model. The concrete realisa-tion of DataFlow depends on the grounding of themeta-model and different means of distinguishing lo-cations and versions of a DomainModel are subse-quently added when concrete values are assigned tothe abstract entities.Figures 2 and 3 illustrate the participants necessaryfor realisation. The model includes process port num-bers, labels and identifiers of processes as well as pre-decessor and successor of a MDO task. Split andJoin tasks are used to model alternative branches inthe control flow.

5.2.2 Realisation of Control Flow

Figure 3 shows a lightweight model of control flow toexpress the role of a predecessor and successor processand also includes specialisations of the general Processentity to distinguish between different types of tasks.

Figure 4 presents a sample overview scenario forthe entities illustrated on the meta-model layer. AMDOTask and a Join process following as a successorto the executed MDOTask. In context of data flowaspects, addressed in Section 5.2.1, Split dispatchesinput values to MDO tasks and Join processes aggre-gate and forward output values from MDO tasks. Inorder to express control flow, we introduce a variablecontrol that is communicated similarly to a regulardata value and is passed on by a Split process eitherto the actual MDOTask or the corresponding substi-tute process. A Join process on the other hand re-ceives control from either of those two processes and

build-cfg

geometry

meshing

solving

filter

retrieve existing

build-cfg result

retrieve existing

geometry result

retrieve existing

meshing result

retrieve existing

solving result

retrieve existing

filter result

execute sub

process

execute fallback

process

switched on?

switched on?

switched on?

switched on?

switched on?

Subprocess

switched on?

Split Node:

Yes No

No

No

No

No

No

Yes

Yes

Yes

Yes

Yes

Figure 4: Schema of Control Flow Realisation

forwards it to the succeeding Split task. In whichof these two possible directions a control variable isrouted currently depends on a manual control the de-signer can manipulate. This dependency is modelledin Figure 4. However, the current realisation doesallow knowledge engineers to introduce more sophis-ticated decision criteria.

5.2.3 Realisation of Grounding

Grounding of the MDOmeta-model incorporates con-cepts required for instance to read and write inputand output data of processes and transform abstractprocesses into executable workflows. To realise agrounding for MDO, an extension of the MDO meta-model is specified that assigns concrete values to asubset of the concepts presented on the meta-modellayer including their respective slots. It therefore as-certains the execution of our abstract model by provi-sion of the concepts that assure a formalisation of theprocess execution environment. Figure 5 shows theMDO meta-model including the link to the domain-ontology layer. Additionally, the Manifestation con-cept is further refined via its constituents URI, For-mat and Revision. The second concept directly asso-ciated with grounding is MDOTool that can representfor instance a concrete engineering application suchas a finite element solver or a complete workflow exe-cution engine. MDOTool inherits from SimpleProcessthe entity that holds the necessary parameter for pro-cess execution including ParameterBindings for inputand output values, a URI denoting to the process ex-ecution path, and, a link to the parent process.

We separate URI into its constituents ’scheme’,’authority’, ’path’, ’query’ and ’fragment’. Thismakes a constraint formulation possible that is basedon URI attributes and serves the purpose of allocat-ing process resources. The URI uniquely locates a re-source such as a domain-model within a file—achievedvia the ’fragment’ attribute that is part of a query—and, secondly, identifies a resource by providing aunique name for it.

We can obtain a representation of an executableprocess model that is sufficiently specified for execu-tion by a particular workflow engine, resulting in aworkflow instance as for example represented in the

54

Figure 5: Grounding of MDO Meta Model Layer

Taverna workflow (Muehlenfeld et al., 2008). Anexecutable model is obtained via grounding of do-main abstraction layer, in conceptual terms, mappingthe domain abstraction layer to the process executionlayer.

5.3 Integration of Ontology Layers

Translation between the intermediate layer andthe ontologies below is accomplished by adaptersthat map between domain-independent and domain-specific representations. The same idea is used toinstantiate abstract process models at the interme-diate level to generate concrete process specificationstailored to specific MDO environments that are subse-quently enacted using a workflow system. In the con-text of grounding of MDO tasks we discussed adaptersas a means of relating Problem Solving Methods toMDO tasks (Fensel, 1997), (Chandrasekaran et al.,1998). Here we will employ adapters as linking el-ements between ontologies on different levels of ab-straction.

5.3.1 Linking Intermediate and Domain Ab-straction Layer

As a means to realise the concept of adapters be-tween intermediate and domain abstraction layer, astrategy can be followed that is based on subsump-tion relations between concepts from these two layers.

To illustrate this mapping mechanism, considertwo representative domains such as meshing and solv-ing that are both covered by the optimisation sce-nario. For the meshing domain we discovered con-cepts required for resource annotation such as mesh-format, meshing-source-code, topology-constructionand meshing-configuration. Similarly, for the solv-ing domain we identified domain terms as for in-stance solving-format, solving-source-code, solving-construction and solving-parametrisation. Theadapter identified by the domain expert can be re-alised by a generalisation relation from concept mesh-format at the domain abstraction layer to the moregeneral concept format at the intermediate layer, and,likewise, from solving-format valid in the solving do-main to concept format realised on the intermedi-ate layer. As a result, two disjoint concepts—mesh-format and solving-format—have been mapped via

a subsumption relation to the concept format at theintermediate layer. This approach can be applied im-mediately to concepts that represent equivalent se-mantics and only differ in the domain covered, as itis the case for example for mesh-format and solving-format.

Domain expertise is required when semanticallydifferent concepts are to be mapped to a commonsubsuming concept as it is the case for instance inmeshing-configuration and solving-parametrisation.In this case, a domain engineer has to support inthe decision whether, firstly, these concepts can beunified with a common super-concept, and, secondly,what terminology should be used for the unifying con-cept. For the given example we decided to use theterm configuration as a subsuming concept, as it wasperceived as the more general concept.

In analogy to the adapter mechanism explainedabove, we can create adapters from a domain-specificMDO task to a generic MDO task on the intermediatelayer.

Consider an example where a domain-specific solv-ing task is detailed. The task is defined as a sub-task of Crashworthiness and requires as input a meshparameter-value and creates result as output value.To develop an adapter to the intermediate layer, weneed to provide a definition of a finite element solverthat is generic enough to represent all possible solverrealisations.

The solving process itself is opaque to the user,only input variables can be changed in a great vari-ety and in addition to ?mesh provided as basic input,parameters such as material properties, section prop-erties, joint stiffness, contacts, boundary conditions,restraints, load curves and further control parameterscan be defined.

We define an input variable ?control-parameterthat acts as an aggregate for all possible parameters ofa solver task. ?control-parameter typically will itselfrepresent a domain ontology that includes terminol-ogy as mentioned above. It is provided as additionalvariable of the solver task to complement ?mesh and?result. To complete the generalisation of LsDyna, werename the domain-specific task to solver and obtaina comprehensive definition of a generic MDO task al-located at the intermediate layer. As an equivalentto the MDO task presented here, an ontology of aproblem solver (Chandrasekaran et al., 1998) can bedefined where a second level ontology denotes to theequivalent of the domain abstraction layer, specifyingthe concepts defined in the first level ontology.

6 Framework Application

We will now outline how the introduced frameworkcan be utilised to support the designer in executionand analysis of MDO scenarios. For this purposewe translate the concepts into a target environmentto validate the parametrisation of a MDO process.We transfer framework concepts to the HierarchicalTask Network (HTN) target platform, in particularthe HTN-like planner Shop2. We provide an imple-mentation of an MDO sample scenario in Shop2 anddecompose a high level formulation of a MDO work-flow into executable process steps. Finally, we pointout lessons learned that have to be considered whenproviding a mapping from MDO to an execution en-vironment and make comments on formal semantics.

55

(:operator (!join ?predecessor ?current ?successor)((process ?predecessor)(process ?current)(process ?successor))((control-at ?current))((control-at ?successor)))

)

Figure 6: Representation of a SimpleProcess in Shop2

6.1 Translation of MDO Framework Compo-nents to Shop2 Notation

We provide a mapping from MDO framework con-cepts to HTN form by detailing how each frameworkcomponent can be realised in Shop2.

MDO SimpleProcess A SimpleProcess in MDO,for instance grounded as a MDOTool, will be repre-sented as an operator in Shop2. Local preconditionsof a SimpleProcess correspond to the operator ’s pre-conditions, the operator ’s add list corresponds to theoutput of a SimpleProcess. Input of a SimplePro-cess is validated and accepted via Shop2 precondi-tions. All input and output objects of a SimpleProcessare available as facts of the knowledge base. Post-conditions of a SimpleProcess are either part of theoperator ’s add- or delete-list. The link to a parentprocess is not directly established in Shop2, however,the parent process—a Shop2 method—includes a linkto its sub-processes. An example for a SimpleProcessrealised as operator is shown in Figure 6. The figureillustrates a simple join process, where the control to-ken is passed between the current and the succeedingprocess. SimpleProcess(es) including their respectivepreconditions and output artefacts can be translatedautomatically to Shop2 notation.

MDO CompoundProcess CompoundProcess(es)in MDO correspond to methods in Shop2. For eachmethod we define alternative branches comprising alist of operators, methods and predicates that areevaluated given the preceding set of preconditionsis true. A CompoundProcess in MDO consists ofone or more SimpleProcess(es) and CompoundPro-cess(es), and, is processed by executing all includedSimpleProcess(es). In MDO, sub-processes of a Com-poundProcess can either be executed in parallel or se-quential. However, Shop2 does not directly supportthe notion of concurrency (Wu et al., 2003). We willneglect this fact for now, as the level of granularitymodelled for the MDO simulation steps only consid-ers sequential tasks.

The semantics of methods in Shop2 prescribes thatexactly one branch, satisfying all pre-conditions, is ex-ecuted. We explain the translation of this MDO com-ponent based on the example depicted in Figure 7:Figure 7 contains two branches, where (trigger ?man-ual) constitutes the precondition for the first branchand (not(trigger ?manual)) represents the precondi-tion of the second branch. If the first precondition istrue, all tasks included in the tail of the branch—forinstance !split, !create-mesh-failover, !join—are exe-cuted.

A CompoundProcess typically represents an algo-rithm or a procedure that comprises a number ofdedicated steps to be completed in order to producea particular result. This algorithm can be imple-mented in different domain-specific ways dependenton the given context. MDO domains are reflected

(:method (simulation-meshing-step ?control ?artefact ?process?manual ?p1 ?p2 ?mesh-format ?mesh-construction?topology-format)(trigger ?manual)

((!split ?p1 ?p2 ?control)(!create-mesh-failover ?mesh-format ?mesh-construction)(!join ?p1 ?p2 ?control))

(not(trigger ?manual))((!split ?p1 ?p2 ?control)(!assign-port ?p ?a)(!create-mesh ?mesh-format ?topology-format ?artefact)(!join ?p1 ?p2 ?control))

)

Figure 7: CompoundProcess in Shop2

(:operator(!create-geometry...)...;add-list of operator(depends-on ?geometry-construction ?geometry-source-code)(depends-on ?geometry-format ?geometry-configuration)(derived-from ?geometry-construction ?geometry-source-code)(created-by ?geometry-format ?geometry-construction-tool)(created-by ?geometry-construction?geometry-construction-tool)))

Figure 8: Local Constraints as Relation between In-put and Output of a MDO Task

as different branches in a Shop2 method where ex-actly one branch—the one corresponding to the givencontext—is executed. A sequence of simple and fur-ther nested MDO tasks can be formulated as a listof operators and methods contained in the tail of aparticular branch. Automated translation of Com-poundProcesses into this format can be supported.

Constraints A pivotal part in transferring theMDO domain representation to Shop2 is the trans-lation of diverse requirements, assumptions and con-straints identified in MDO and formulated as con-straints. Figure 8 shows how local constraints of anMDOTask are expressed as preconditions of a Shop2operator.

Figure 8 also includes constraints that relate inputand output of an operator. Relations between inputand output of tasks support the concept of traceabil-ity of MDO artefacts and processes by tracing of de-pendencies between input and output.

The predicates shown in Figure 8 are part of theadd-list of an operator.Further integrity constraints can be expressedthrough the formulation of axioms to define globalrestrictions all instances of the problem domain arebound to. Axioms in Shop2 are evaluated either aspart of other axioms or in preconditions of Shop2methods.

Ports Ports are represented in Shop2 by variablenames defined to hold particular types of processinput and output, typically corresponding to MDOartefacts passed to a process. They can validate pro-cess input and only variables of the defined types areaccepted when starting the planning process.

56

(:method (mdo-workflow ?control ?process-id?p1 ?p11 ?port1 ?art-1 ?res-1 ?aut-1?p2 ?p22 ?port2 ?art-2 ?res-2 ?aut-2?p3 ?p33 ?port3 ?art-3 ?res-3 ?aut-3?p4 ?p44 ?port4 ?art-4 ?res-4 ?aut-4?p5 ?p55 ?port5 ?art-5 ?res-5 ?aut-5)()((simulation-build-config-step?control ?p1 ?p11 ?port1 ?art-1 ?res-1 ?aut-1 ?process-id)

(simulation-create-geometry-step?control ?p2 ?p22 ?port2 ?art-2 ?res-2 ?aut-2 ?process-id)

(simulation-meshing-step?control ?p3 ?p33 ?port3 ?art-3 ?res-3 ?aut-3 ?process-id)

(simulation-solving-step?control ?p4 ?p44 ?port4 ?art-4 ?res-4 ?aut-4 ?process-id)

(simulation-filter-response-step?control ?p5 ?p55 ?port5 ?art-5 ?res-5 ?aut-5 ?process-id)

))

Figure 9: MDO Workflow as Composite Process

DataFlow Process output can be represented inShop2 via the produced effects, available as facts inthe current state of the world. Process input is for-malised via preconditions. As a predicate to furthersupport the notion of process input and output we de-fine the primitive instance-of that takes as argumentsthe current operator instance, the created concept orattribute, and, an ID, unique per simple process andused for tracing of output of subsequent process steps.

Artefacts Each input and output of a Shop2 op-erator corresponds to an artefact from the MDO do-main. In addition, each artefact has a manifestationattached, pointing to its physical location. Individualtypes of artefacts are defined via predicates that areavailable as logical primitives in operators, methodsand axioms. Relations between these artefacts, suchas constraints, can be defined in axioms and are addedin the body of a Shop2 method definition. Artefactsproduced as output of a process are part of the cur-rent planning state and each precondition of a fol-lowing Shop2 method or operator will be evaluatedagainst this globally available state.

6.1.1 Top-Down Formulation of ExecutableMDO Workflow in Shop2

For a complete formulation of the MDO workflow inShop2, the translated components are parametrisedand combined into a high level method. The resultingconstruct represent the planning goal of Shop2 thathas to be solved by the planner.

The top-level Shop2 method is illustrated in Fig-ure 9. As the complete implementation of this samplespawns several pages, only snippets of the source codefor the planning problem are depicted.

The refinement strategy for the abstract workflowis predefined by the decomposition mechanism of theplanner. The decomposition of the MDO workflowstarts with the most abstract method mdo-workflowthat is added to the plan and broken down intocompound and simple tasks, in Shop2 terminology,methods and operators. The top-level methodmdo-workflow can be broken down into the followingShop2 methods:

simulation-build-config-step,simulation-create-geometry-step,simulation-meshing-step,

(:method (simulation-meshing-step ?control ?p1 ?p2?p ?a ?resource ?aut ?process-id)

(not(trigger ?aut))((!!init ?process-id)(!split ?p1 ?p2 ?control)(!create-mesh-failover ?mesh-format?topology-format ?mesh-construction ?resource)(!join ?p1 ?p2 ?control)

)(trigger ?aut)

((!!init ?process-id)(!split ?p1 ?p2 ?control)(!assign-port ?p ?a)(!create-mesh ?p ?a ?control ?process-id)(!join ?p1 ?p2 ?control)

))

Figure 10: Simulation Meshing Process in Shop2

simulation-solving-step, andsimulation-filter-response-step

These correspond to the simulation processes, build-cfg, create-geometry, meshing, solving and filter-response. However, these sub-processes represent asuper-set of the basic simulation processes, as controlflow as well as a failover process are combined in thehigh-level process.

The workflow formulation illustrated in Figure 9comprises all parameters required to execute the sim-ulation, assuming that effects resulting from execu-tion of individual operators are available as state in-formation that is taken as input for the respectivesubsequent processes.As an example for the next highest layer of abstrac-tion, the method simulation-meshing-step is detailed.The method, allocated at the intermediate layer ofthe MDO framework, represents a domain indepen-dent version of all meshing procedures that can beexecuted as part of MDO scenarios. For a mappingfrom the intermediate layer to the domain-abstractionlayer we add details such as tool-information andother environment specific knowledge, that estab-lishes a binding to a given execution environment.

The method shows two branches that produceequivalent results. The second branch depicted con-tains the Shop2 operators !!init, !split, !assign-port,!create-mesh and join. All tasks listed are eitherMDO SimpleProcess(es) or they are Shop2 internaltasks performing supporting activities. In Shop2 ter-minology this means all tasks contained in methodsimulation-meshing-step can be directly executed andare not further decomposed. The method displayed isa simplified configuration for an MDO scenario. Fur-ther specifications for each included domain have tobe added that represent the various domain-specificalgorithms and tools that can be configured when us-ing method simulation-meshing-step.

6.2 Support of workflow consistency checkingby decomposition in Shop2

We now elaborate on a concrete use case with the ob-jective to demonstrate how the ontology frameworkcan be applied to support engineering design scenar-ios. The addressed problem can be described as fol-lows: an experienced design engineer typically com-poses a design optimisation scenario by taking ad-

57

<!-- PROCESS configuration formulation -->

<process-configuration process= "create-geometry" cluster = "karros.autocrc.com" platform = "sun-solaris-10.4.2" >

<process name = "create-geometry" parent = "mdo-simulation" simple-process = "false" type = "mdo-task">

<sub-process name = "read-geometry-definition"/>

<sub-process name = "read-geometry-configuration"/>

<sub-process name = "parametrise-geometry"/>

<port id = "Bi1" process = "create-geometry" type = "input"

parameter-description = "geometry-configuration ^ geometry-construction ^

geometry-source-code ^ meta-data ^ manifestation"

constraints = "/karros.autocrc.com:mdo-simulation-cb1:create-geometry:Bi1"/>

<port id = "Bi2" process = "create-geometry" type = "input"

parameter-description = "geometry-configuration ^ meta-data ^ manifestation"

constraints = "/karros.autocrc.com:mdo-simulation-cb1:create-geometry:Bi2" />

<port id = "Bo5" process = "create-geometry" type = "output"

parameter-description = "geometry-format ^ STEP-format ^ solid-model-format ^ CAD-format"

constraints = "/karros.autocrc.com:mdo-simulation-cb1:create-geometry:Bo5" />

<error type = "input-mismatch" message = "input mismatch error" />

<error type = "cluster-unavailability" message = "cluster unavailable error" />

<error type = "output-mismatch" message = "output mismatch error" />

<error type = "external-dependency" message = "external dependency error"/>

</process>

</process-configuration>

Figure 11: Executable MDO Process description ininternal xml format

vantage of an existing repository of process modelsthat represent successfully performed tasks on designartefacts. However, as the given problem descrip-tion distinguishes from previous scenarios, these pro-cess traces have to be reparametrised in order to suitthe given situation. For example, due to a changedmodel size a different hardware component might berequired in order to execute a particular solving ap-plication. In another case, a mass optimisation sce-nario might imply a switch to a different geometryformat that is not part of a standard setup. In or-der to avoid the execution of a design scenario thatconsumes extended resources and due to constraintsdescribed above, finally fails, we want to check a givenconfiguration in advance to improve the probability ofa successful workflow execution. For this purpose weutilise Shop2 and realise workflow consistency check-ing by implementing the concepts represented in theMDO ontology framework.

Shop2 will be applied for the decomposition of areparametrised MDO workflow into executable plan-ning steps, showing that a consistent workflow re-finement is possible. The difficulty in this task isthe selection of value assignments for the includedconstraints, i.e., managing the trade-off between cre-ating a too restrictive configuration that implies alow probability that a plan—corresponding to a validworkflow decomposition—can be found, and, select-ing the assignments for the participating parameterstoo generic, i.e., risking that too many plans are foundby the planner. We assume the following setup for aworkflow consistency checking scenario:

• An instance and parametrisation of an MDO pro-cess is given as shown in Figure 11. The Figureillustrates the individual process steps and theparameter assignments per sub-process.

• For a new similar MDO scenario, a designer canselect existing process traces from a repository ofprocess models that have been used previously.The selection of these components is based onthe number and type of parameters contained inthe process model.

• The new parametrisation for the MDO workflowto be executed is transferred to the selected pro-cess models

• The new configuration can be checked for consis-tency with Shop2 and a reasoner can be appliedfor detecting violations of integrity constraints.

(:method (create-geometry ?control ?cluster ?platform ?workflow-engine ?revision

?parent-process ?simple-process ?type ?errors

?port-id_1 ?process_1 ?type_1 ?parameter-description_1

?constraints_1 ?address_1 ?manual_1

?port-id_2 ?process_2 ?type_2 ?parameter-description_2

?constraints_2 ?address_2 ?manual_2

?port-id_3 ?process_3 ?type_3 ?parameter-description_3

?constraints_3 ?address_3 ?manual_3)

()

((read-geometry-definition ?port-id_1 ?process_1 ?type_1

?parameter-description_1 ?constraints_1 ?address_1 ?manual_1)

(read-geometry-configuration ?port-id_2 ?process_2 ?type_2

?parameter-description_2 ?constraints_2 ?address_2 ?manual_2)

(parametrise-geometry ?port-id_3 ?process_3 ?type_3

?parameter-description_3 ?constraints_3 ?address_3 ?manual_3))

Figure 12: MDO Sub-Process create-geometry asShop2 method

Assume an instance of the MDO workflow is givenby the following generic description - only the sub-process create-geometry is illustrated for space rea-sons: all parameters of the workflow descriptionare grounded, i.e., they possess a valid parameter-binding. Deriving a new workflow instance froman existing one means modifying some of the value-assignments of the original workflow instance to suitthe context of the new scenario. However, what typi-cally causes errors are implicit dependencies betweenparameters, that are not considered when modifyingexisting value assignments.

Shop2 either decomposes a high level abstract pro-cess into executable operators and methods (that is,it checks whether a plan can be found), or, alterna-tively, it can validate whether a high level represen-tation exists that corresponds to a given executiontrace of an MDO scenario. For the latter, the ex-ecution trace is translated into Shop2 constructs asexplained above and correspondences between theseconstructs and high level Shop2 methods are inves-tigated. Both approaches can be utilised for consis-tency checking of MDO workflows. We will demon-strate how Shop2 is applied for workflow consistencychecking by top-down decomposition of a given Shop2goal formulation that corresponds to a given MDOexecution trace.

After the reconfiguration for the new situation hasbeen completed, the description will be transformedinto Shop2 notation and the modified parameters areupdated in the high-level representation of the MDOworkflow. The corresponding formulation of the newworkflow in Shop2 is shown in Figure 12.

We can demonstrate consistency of the new work-flow by showing that the planner is able to find aplan that corresponds to an executable workflow. Ifno plan can be found, an inconsistency in the work-flow representation exists.

As an example for an inconsistency that can bedetected in this way, consider the modification of pa-rameters that represent the model size of a geome-try model. As a typical MDO environment comprisesa number of alternative MDO tools for a particularMDO task, a different MDO tool is assigned depen-dent on model characteristics. For instance the MDOtask create-mesh can require are different meshing-tool dependent on parameters such as model-size andmesh-size. Using a different meshing tool can alsoimply that subsequent process steps have to be exe-cuted with different software components, dependenton the product used in the meshing step, resultingin an alternative execution path that was not consid-ered by the designer when modifying the model sizebut keeping all remaining components in place.

58

To summarise, our reuse scenario is based on his-toric process execution traces that are parametrisedaccording to the given design task. When reconfigur-ing a given trace by assigning a different parametervalue, an inconsistent parametrisation of a process in-stance can result due to dependencies not consideredby the designer. Shop2 can support in elimination ofthese inconsistencies by simulating the process execu-tion, i.e., calculating whether a plan can be found forthe new configuration.

6.2.1 Summary on Process Refinement

The technical realisation of the MDO workflow re-finement in Shop2 demonstrated that the conceptscomprised in the ontology framework can support aconcrete design scenario. By utilising technologiesfrom the planning domain, MDO process decompo-sition can be simulated with the objective to supportthe designer in the configuration process of a designscenario. As a future work, Shop2 models can beconsidered for translation into an executable work-flow model, available in a target workflow language,provided the semantics of the target formalism can berepresented in Shop2. Another aspect is the degreeof automation that can be achieved when translatingMDO tasks into Shop2 notation.

7 Conclusion

The introduced ontology framework can support typ-ical activities of design engineers and enable them tomore effectively use and explore results of an MDOscenario. The framework, comprising componentssuch as domain and execution layer, domain abstrac-tion layer as well as an intermediate and meta-modellayer, addresses the integration of engineering pro-cesses by mapping and interrelating the developedconcepts. Techniques from the planning realm havebeen utilised to demonstrate how our ontology frame-work can be applied to support the detection of work-flow inconsistencies.

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Appendix A: MDO Domain Model

-mesh_size : SU

-solver_input_file : File

-solver_template : solver input template

-offset_mass_node : SU

-mass_node_ID : string

-component_name : string

-translator_file_type : format

-mass : SU

-run_name : string

-mdo_job : simulation type

-meshing_modus : string

-mesh_completion_status : integer

meshing configuration

-component_...

meshing

source code

topology

construction

topology

cleanup

geometry

construction

geometry

format

topology

format

-geometry_creation_tool : path

-mesh_creation_tool : path

-tool_exec_paths : set[path]

workflow configuration

mesh

format

-manifestation : manifestation

-meta_data : meta-data

-source_code : source code

<<domain model>>

configuration

-manifestation : manifestation

-meta_data : meta-data

-source_code : source code

-tool : Tool

<<domain model>>

construction

-manifestation : manifestation

-meta_data : meta-data

-format_version : version

-text : boolean

<<domain model>>

format

-name : string

-manifestation : manifestation

-meta_data : meta-data

-category : artefact category

-purpose : function[]

-artefact_construction : set[construction]

-artefact_configuration : set[configuration]

-artefact_representation : set[representation]

Artefact

-manifestation : manifestation

-meta_data : meta-data

-language : programming language

-copyright : copyright

<<domain model>>

source code -manifestation : manifestation

-meta_data : meta-data

-name : string

-features : set[tool_feature]

-tool_type : tool type

-input : set[ParameterBinding]

-output : set[ParameterBinding]

-path : string

-documentation : documentation

-accepted_formats : set[format]

-vendor : tool vendor

tool

-creation_date : date

-modification_date : date

-comment : string

-purpose : string

-creator : person

-owner : person/organisation

-creation_tool : tool

-creation_tool_type : tool-type

-documentation : documentation

<<domain model>>

meta-data

-run_name : string

-component_geometry : SI

-feature_geometries : set[feature_geometry]

-assembly_geometry : csg geometry

-feature_geometry : set[simple_geometry]

-CSG_geometry : set[simple_geometry]

-simple_geometry : set[SU]

geometry configuration

geometry

source code

solving

source code

-uri : URI

-format : format

-revision : revision

<<abstract concept>>

<<trait>>

Manifestation

-incl_cards : card[]

-velocity : SU

-solver_mass : SU

-wall_d : SU

-est_time : SU

solving

configuration

simulation

source code

geometry

cleanup

solver input

deck

+response_file_set : set[file]

+design_objective : objective

-manifestation : manifestation

-meta_data : meta-data

<<domain model>>

solving response

response

raw -type : type

-dimension : integer

-filter : response filter

response filtered

response

binary

response

text

filtering

source code

-manifestation : manifestation

-meta_data : meta-data

-mesher_version : version

-copyright : string

-mesher_keywords : source code

-solver_keywords : source code

solver input template

<<domain model>>

translation map

hypermesh lsdyna map

response filter

-algorithm : analysis methodology

-result_data : analysis result

<<domain model>>

analysis model

pca model

rsm model

pareto frontier model

material

format

Component

Assembly

documentation

format

assembly

format

vertex model

format

parametric

model format

csg format b-rep format

analysis model

format

time stamp

statistics

energy

statistics

force

statistics

memory

consumption

statistics

response

data

element

data

nodal point

data

material

energy

statistics

discrete

element forces

wall forces nodal

constraint

reaction forces

cross section

forces

global data

response energy

ab_statistics sliding

interface

energy

joint forces

plotting

response

simulation

restart

geometry

creation tool

meshing tool solving tool

mesh

construction

solver result

construction

1..*

0..*

hasConfiguration

0..1

hasTranslationMap

hasSolvingResponse

is-represented-by

hasAnalysisModel

hasMetaData

created-by

is-represented-by

hasRepresentationFormat

is-constructed-by

Figure 13: MDO Domain Model

60

Ontology Inferencing Rules and Operations in Conceptual Structure

Theory

Philip H.P. Nguyen1, Ken Kaneiwa

2 and Minh-Quang Nguyen

3

1 Justice Technology Services, Department of Justice, Government of South Australia 30, Wakefield Street, Adelaide, SA 5000, Australia

2 Department of Electrical Engineering and Computer Science, Iwate University 4-3-5 Ueda, Morioka, Iwate 020-8551, Japan

3 University of Quebec at Montreal, 405, rue Sainte-Catherine Est, Montréal (Québec) H2L 2C4, Canada

philip.nguyen@sa.gov.au, kaneiwa@cis.iwate-u.ac.jp, nguyen.minh-quang@uqam.ca

Abstract

This paper describes in detail the inferencing rules and operations concerning an ontology formalism previously proposed under Conceptual Structure Theory. The ontology consists of hierarchies of concept, relation and meta-relation types, and formal relationships between them, in particular between arguments of relation and meta-relation types. Inferencing rules are described as well as operations to maintain the ontology in a semantically consistent state at all times. The main aim of the paper is to provide a blue print for the implementation of ontologies in the future Semantic Web. 1

Keywords: Knowledge representation, ontology, automated reasoning, graph theory, type theory, Conceptual Structure Theory, Semantic Web.

1 Introduction

The implementation of an ontology is the basis for the development of any semantic inferencing applications, such as semantic web search engines and query-answering systems. This paper proposes to comprehensively describe all the inferencing rules and operations concerning an ontology formalism previously published under Conceptual Structure Theory (Nguyen and Corbett Feb./Aug. 2006, Nguyen et al. Oct./Dec. 2009). The mathematical foundation of the theory is translated into a detailed and practical process to implement an ontology for any domain of discourse. The main aim of the paper is to provide a blue print for implementation of a complete and sound ontology serving as the backbone for a semantic inferencing system. The contribution of this paper to knowledge representation is two-fold: firstly, an ontology formalism under Conceptual Structure Theory is reviewed, enhanced, and presented in a simplified manner to facilitate understanding, and secondly, inferencing rules on the ontology are detailed with their usage clarified, so that inferences could be performed whenever required. A semantically consistent state of the ontology is maintained at all times. This means that each time an

Copyright © 2010, Australian Computer Society, Inc. This paper appeared at the Sixth Australasian Ontology Workshop (AOW 2010), Adelaide, Australia. Conferences in Research and Practice in Information Technology (CRPIT), Vol. 122. Thomas Meyer, Mehmet Orgun, and Kerry Taylor, Eds. Reproduction for academic, not-for-profit purposes permitted provided this text is included.

update is performed on any object of the ontology, all the semantically related objects and structures are also reviewed and updated so that the ontology complies at all times with all the rules of the ontology formalism.

According to a formalism in Conceptual Structure Theory, an ontology consists of three partially ordered sets of concept types, relation types, and meta-relation types, a set of individuals (which are instances of concept, relation and meta-relation types), and logical rules concerning semantic relationships between those structures, objects and their attributes. An ontology could be considered a specific form of organizing a knowledge base, or a knowledge representation extension of a traditional database. The main difference with the latter is that both public and private information is maintained in the ontology. For example, in a criminal justice administration ontology, private information on offenders and victims is recorded, as well as public information such as criminal law codes. The type hierarchies in the ontology are generally public information and often meant to be shared across different applications in the same domain of discourse. They usually represent common knowledge agreed to by domain experts and are not built with a specific application in mind. Dynamic and specific information such as names and addresses of individuals is traditionally maintained in a separate database, e.g., a customer and billing database in a commercial company, or an offender database in a criminal justice system.

Inferencing rules are also detailed on the proposed ontology formalism, including knowledge consistency checking, a feature similar to that of Description Logics (DL) (Horrocks 1999).

This paper is organized as follows: Section 2 reviews and consolidates the ontology formalism previously proposed within Conceptual Structure Theory with particular emphasis on the logical rules that enable inferences on such an ontology, Section 3 describes the mathematical properties of the ontology formalism, and Section 4 concludes the paper.

2 Ontology Formalism under Conceptual

Structure Theory

An ontology formalism has been proposed under Conceptual Structure Theory (Nguyen and Corbett Feb./Aug. 2006, Nguyen et al. 2008), with the concepts of meta-relation and hyper-predicate being most recently incorporated (Nguyen et al. Dec. 2009, Kaneiwa and

61

Nguyen 2009). This paper consolidates the previous work and rationalizes its inferencing rules, with the view of applying it to practical domains. In particular, mathematical properties are translated into simple natural language statements and backed up by examples to assist with understanding.

The proposed ontology formalism essentially consists of two components: a formal definition of ontology and a set of axiomatic-semantics rules for reasoning and inferencing.

2.1 Basic Definitions

Following is the broadest definition of an ontology according to Conceptual Structure Theory.

2.1.1 Ontology Definition

Definition 1 (Ontology). An ontology O is a 5-tuple O =

(T, I, �, conf, B) in which:

(1) T is the set of types, i.e., T=TC∪TR∪TMR with TC

being the set of concept types, TR the set of relation types, and TMR the set of meta-relation types. In simple terms, a concept type is a class of objects, a relation type is a predicate on concept types and a meta-relation type is a predicate on relation types and concept types. By definition, a meta-relation type connects at least one relation type and any number of concept type. The fictitious Top and Bottom types (denoted by “T” and “⊥”) are supposed to be included in each set for mathematical completeness. By convention, the label (or name) of a concept type is a noun and written with the first character in upper case (e.g., Offender, Victim) while that of a relation or meta-relation type is a verb conjugated in the third person singular and written with the first character in lower case (e.g., steals, isMarriedTo).

(2) I is the set of individuals, or instances of concept, relation and meta-relation types in T, i.e.,

I=IC∪IR∪IMR with IC being the set of instances of concept types (also simply called concepts), IR the set of instances of relation types (also simply called relations), and IMR the set of instances of meta-relation types (also simply called meta-relations). The notion individual used in this paper is generic and denotes any real-life person, object or situation. Its true meaning is an instance of a class or type.

(3) The symbol “�” is the subsumption relation (or

semantic subsumption relation) in T, i.e., � is a

subset of (TCxTC)∪(TRxTR)∪(TMRxTMR), representing the semantic generalization or specialization relationship between two concept types, two relation types or two meta-relation types. For example, Man

� Person because Person is a generalization of Man, or Man is a specialization of Person. The subsumption relation induces a partial order on T.

(4) The symbol “conf” is the conformity function, defining for each individual in I, the infimum (or greatest lower bound) of all concept, relation or meta-relation types that could represent that

individual, i.e., conf: I → T with ∀c∈IC conf(c)∈TC ,

∀r∈IR conf(r)∈TR and ∀mr∈IR conf(mr)∈TMR . For example, conf(John)=Man as Man is the infimum of

all concept types such as LivingEntity, Person, Man, etc. that could represent John. For a relation or meta-relation, the value of conf is simply the relation or meta-relation type that is used in that relation or meta-relation, i.e., conf(isSonOf(John, Peter))= isSonOf(Person,Man). Since a type is a class and an individual is an instance of that class, as a convention, it is also

written x∈X when the individual x is of type X, i.e.,

∀x∈IC∪IR∪IMR conf(x)=X ⇔ x∈X. (5) The symbol “B” is the canonical basis function,

defining the usage model or usage pattern of a relation or meta-relation type (the word canon means model). B associates each type in TR with a tuple of concept types, called relation type arguments, that can be used in that relation type, and each type in TMR with a tuple of relation and concept types, called meta-relation type arguments, that can be used in that meta-relation type. For example, isDaughterOf(Female, Person) is a relation type linking two arguments of which the first (the concept type Female) is the daughter and the second (the concept type Person) is the parent. Formally, B:

TR∪TMR → τ(TC)∪τ(TR∪TC) with τ(X) being the set of all tuples defined over the set X, i.e., τ(X) =

∪{n>0}(X)n. As a convention, an element x of a tuple T

is written as x∈T (see also Sect. 3). The number of arguments of a relation type is also called the valence or arity of the relation type.

2.1.2 Basic Ontological Rules

Definition 2 (Ontological Rules). The above ontology definition is underpinned by the following basic rules: (1) Type Label Uniqueness Rule: Each concept type in

the ontology must be semantically unique. This rule enables T to be defined as a mathematical set (as each member of a set must be unique inside the set). As a notation, two semantically identical (or synonymous) types X and Y is written as X ≡ Y.

(2) Argument Label Uniqueness Rule: Each argument label of a relation or meta-relation type must be semantically unique within the set of all arguments of that type hierarchy. This rule means that the above rule on uniqueness of type labels also applies to arguments of relation and meta-relation types. In addition, the argument labels should also reflect the meaning of the argument in the relation or meta-relation type, as in the example below.

Example 1: If isChildOf(Person, Person) is defined as a relation type in which the first person is the child and the second person is the parent, then it should be noted that the semantics of the two persons in that relation type are different and therefore they should be uniquely distinguished. This could be done by giving a different index to each argument, such as isChildOf(Person1, Person2) with Person1 defined as the child of Person2. Those new argument labels should then be consistently used for any new relation type requiring similar semantics in its arguments. Also, as per the Type Label Uniqueness Rule, which applies to all types in the ontology, it is not possible to have in the same ontology, relation types and

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arguments such as isChildOf(HumanBeing1, Person2) or isOffspringOf(Person1, Person2) (because isChildOf ≡ isOffspringOf and HumanBeing1 ≡ Person1).

(3) Conformance rule: The infimum of any two (concept, relation or meta-relation) types must exist in the ontology and must be unique. This rule enables conf to be defined as a (mathematical) function, as it relies on the existence of a unique infimum for any subset of concept, relation or meta-relation types. (Note that that infimum could be the Bottom type.) This also means that TC , TR and TMR are semi-lattices. This assumption is common in ontology formalization, such as in Formal Concept Analysis (Wille 1982, Stumme 2002) and Order-Sorted Logic (Kaneiwa 2004), for mathematical soundness and completeness.

(4) The word tuple used in the tuple of arguments of a relation or meta-relation type is mathematically defined as a semantically ordered multi-set. A multi-set is a set in which duplicate members are allowed, while “semantically ordered” means that the order of listing of the members of the multi-set is significant. In other words, the semantics of each argument as well as its listing order in the tuple contribute to the semantics of the relation or meta-relation type. For example, the relation type isChildOf(Person, Person) is a relation type with two arguments of the same label Person, in which the first argument is the child and the second argument is the parent. So, the relation isChildOf(John, Peter) is semantically different from the relation isChildOf(Peter, John). The following rule (the B-rule) ensures that arguments and their listing orders in argument tuples are consistently defined between subsuming and subsumed types.

(5) The semantic relationship between (relation and meta-relation) type subsumption and argument subsumption is expressed as a rule over the function B, called the B-rule:

B-rule: ∀S,R∈TR∪TMR with B(S)=<a1,…,an>,

B(R) = <b1, …,bm> and S � R

∀k ≤ m ( ∃i ≤ n ai � bk ⇒ ∀h>k ∄j<i aj � bh )

which could be translated as: If R subsumes S and if there is an argument of R that subsumes an argument of S, then any other higher order argument of R cannot subsume a lower order argument of S, with a higher (resp. lower) order argument being an argument listed after (resp. before) the argument being considered, in the tuple of arguments. It can also be proven that the second line of the B-rule is equivalent to:

∀i ≤ n (∃k ≤ m ai � bk ⇒ ∀j>i ∄h<k aj � bh )

which could be translated as: If R subsumes S and if there is an argument of S that is subsumed into an argument of R, then any other higher order argument of S cannot be subsumed into a lower order argument of R. In simple terms, the B-rule means that: “Each argument of a supertype subsumes the corresponding argument, if exists, of a subtype”, or “Each argument of a subtype is subsumed into the corresponding

argument, if exists, of a supertype”. Example 2: If the subsumption relation

steals(Thief) � offends(Offender, Victim) exists in the ontology, then the first argument (Offender) of the relation supertype must subsume the first argument (Thief) of the relation subtype, while the second argument (Victim) of the supertype is ignored as there is no corresponding argument in the relation subtype. But if the ontology contains instead the

subsumption relation steals(Thief) � offends(Victim) then the B-rule is ignored as the two arguments (Thief and Victim) have different semantics inside the two types.

(6) Argument Tuple Consistency: The orders in which arguments are listed in the tuples of arguments of the subtype and supertype of the new subsumption relation must respect the B-rule, that is, the supertype arguments must subsume the subtype arguments in their respective orders. This rule in essence translates the B-rule into the syntax of the argument tuples of the subsuming and subsumed types.

Example 3: Suppose that isChildOf(Person1, Person2) is an existing relation type (Example 1) and a new relation subtype is identified as isSonOf(MalePerson, Person), in which the first person is the son and the second person is the parent. The semantics of the second argument in both relation types is the same and consequently the second relation type should use Person2 as one of its arguments. In addition, to respect the B-rule, it should be written as isSonOf(MalePerson, Person2), and not isSonOf(Person2 , MalePerson).

(7) Subsumption cyclic consistency check: A type cannot subsume itself through cyclic subsumption relations. In general, this rule is always satisfied if the ontology is maintained at all times in accord with a sound semantic lexicon used as an upper reference ontology. In this case, there should be no inconsistency in type subsumptions between the lexicon and the type hierarchies. In particular, the type hierarchies cannot be cyclic, i.e., containing a type that subsumes and is subsumed at the same time in another type, unless the lexicon is inconsistent in itself. However, if this possibility is allowed, then the rule is necessary.

(8) When all the arguments of a subtype are subsumed into the corresponding arguments of a supertype, the subtype is said to be syntactically (as well as semantically) subsumed into the supertype. In the two cases of Example 2, the former is a semantical as well as syntactical subsumption relation while the latter is a semantical-only subsumption relation. When two relation or meta-relation types are semantically identical and have the same label, but one has more arguments than the other, the former is said to be an extended type of the latter and is written with a superscript “^” at the end of the type label.

2.1.3 Type and Instance Property

Definition 3 (Property). In an ontology, any piece of information intrinsic to the ontology that cannot be

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classified in one of the existing ontological objects (as in Definition 1) should be recorded as a new attribute to an existing type or instance. This attribute is called a property of that type or instance.

The type or instance to which the property is added should be selected depending on the intensional meaning of the extra information and its relevance to that type or instance. In traditional databases, this type of unclassified information is simply recorded as free-text notes attached to database subjects. Property is a way to record unclassified information on which reasoning and inferencing may need to be performed. This is assisted by rules governing the propagation of properties between ontological objects. As a convention, properties are written between square brackets following the type label and arguments (if exist).

Example 4: If the law of a country imposes a minimum jail term of 3 years for any murder, and the ontology contains a relation type murders(Offender, Victim), then the extra information could be added as a property of the relation type murders and written as murders(Offender, Victim, <minimumJailTerm: 3 years>). This property could then be propagated to all instances of the relation type murders.

Definition 4 (Instance Subsumption). Subsumption is a notion originally pertaining to (concept, relation and meta-relation) types only. This paper extends this notion to type instances. By definition, an instance v of a type V is said to subsume an instance u of type U (or u is

subsumed into v) and it is written u � v if v semantically generalizes u (or u semantically specializes v). This latter

condition means that U � V and all the properties and arguments (if exist, i.e., in case of relation and meta-relation types) of v are specialized into corresponding properties and arguments of u (or those of u generalized into those of v). Note that the subsumption notion is also extended into argument tuples (see Sect. 3).

In summary, concept types and instances may have properties, while relation and meta-relation types and instances have arguments and may have properties. In addition, arguments of relation and meta-relation types (or instances) may include concept types (or concepts), which may have properties of their own. Different rules govern the way those arguments and properties are propagated between ontological objects. An argument or property is said to be inherited by a type or instance when that argument or property is added as is, to that type or instance. In addition, if that argument or property is merged with the semantics of the type or instance to become a more generalized or specialized piece of information of the type or instance, then it is said to be generalized or specialized by the type or instance (depending on whether the information is propagated from a subtype, a subtype instance, a supertype, or a supertype instance - See Examples 8 and 9).

Example 5: In Example 4, if the existence of a Police record is always assumed for any offender, then the property <hasPoliceRecord> could be added as a property to the concept type Offender, and when an instance of the relation type murders is added to the ontology, it could be inferred that any offender will

receive a sentence of at least 3 year jail term and has (or will have) a Police record. Note that the property <minimumJailTerm: 3 years> is a property of the relation type murders rather than of the concept type Offender because that property is mainly related to that instance of murder rather than to the murderer, e.g., the murderer may have committed other offences, each may carry a different penalty, which will be added to that person’s sentence. This example shows that the semantics of the arguments of a relation (or meta-relation) type contributes to the semantics of the relation (or meta-relation) type itself.

2.1.4 Event Assertions In real life, sometimes it is not easy to classify new information into existing types, especially when the information is complex and is best described in natural language. One such case is event assertion, which is a description of an event or a state of anything. In traditional databases, this information is usually recoded as free-text notes attached to the main objects identified in the assertion, when this identification is possible. Otherwise, the main objects are arbitrarily chosen. Inferencing from these event assertions can then only be performed by human experts.

To enable automated inferencing on event assertions, a process based on the use of an upper event ontology has been proposed to formalize event assertions as new and/or existing types and instances of the ontology (Kaneiwa et al. 2007, Nguyen et al. Oct. 2009). Depending on the application, the upper ontology may vary from domain to domain. For example, for reasoning with financial fraud, it is recommended to use SUMO’s (Suggested Upper Merged Ontology’s) financial ontology and ontology of services, and McCarthy’s REA (economic Resources, economic Events, and economic Agents) ontology (Kingston 2004).

Note that in Conceptual Structure Theory, the main idea of formally representing event assertions is to transform them into conceptual graphs (Sowa 2000) using concept, relation and meta-relation types as defined above. Conceptual graphs can represent any assertion, not just event assertion, but in most applications, useful information often concerns an event or a fact, which in its broadest definition is anything that has occurred. One of the important features of a conceptual graph is that it is bipartite, that is, any concept can only be connected to another concept through a relation, and similarly, any relation can only be connected to another relation through a concept. This feature is broadened in this paper with the introduction of meta-relation, which did not exist in the traditional definition of a conceptual graph. In this case, the bipartite property of a conceptual graph could be expressed as: a concept can only be connected to another concept through a relation or meta-relation, a relation can only be connected to another relation through a concept or meta-relation, and a meta-relation can only be connected to another meta-relation through a concept or a relation.

2.2 Inferencing Rules

Type subsumption defines a relationship between a subtype and a supertype. That relationship contributes to

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the semantics of both types and therefore should enable some semantics of one type to be transferred to the other, such as in the case of relation and meta-relation types where the extra arguments of one type can be transferred to the other. This is one of the main ideas behind the process of completing missing arguments in a relation or meta-relation type, which is essential for inferencing in some cases.

Inferencing is also most useful when applied to real-world objects and events, that is, when it is performed on the set of individuals in the ontology.

Semantic axioms can improve reasoning over the ontology (Nguyen et al. Dec. 2009). In the case of the proposed ontology formalism, inferencing axioms (also called rules) include the following ones.

2.2.1 Type Argument Generalization

This rule concerns relation and meta-relation types and states that:

∀S,R∈TR∪TMR with S � R, ∀a∈B(S) (∄b∈B(R) a�b)

⇒ (∃R^∈TR∪TMR ∃c∈TC∪TR such that R^ ≡ R,

B(R)⊂B(R^), arity(R^)=arity(R)+1, c∈B(R^) and a�c)

which could be translated as: “Any argument of a subtype can be generalized into a new argument of a supertype, if the latter argument did not exist”. See also Def. 6 on tuple extension.

Note that the B-rule already states that any subtype argument is subsumed by a corresponding supertype argument, if the latter exists. The new rule states in addition that if the latter did not exist then it could be created as a new argument of the supertype by generalizing the subtype argument. The main difference between the B-rule and this new rule is that the former simply verifies semantic consistency between type subsumption and argument subsumption (i.e., subtype arguments must be subsumed in corresponding supertype arguments, if exist) while the latter in addition could create new arguments for the supertype (i.e., subtype and supertype could have the same number of arguments and subtype arguments are subsumed in corresponding supertype arguments). Thus, subsumption enables some semantics of the subtype to be transferred to the supertype, through the enrichment of the arguments of the latter. The enriched supertype is then called the extension of the initial supertype with respect to the subtype. For

example, if S and R are two relation types with S � R, then the arguments of S could be transferred into R to produce a new supertype with enriched arguments, called the extension of R with respect to S and denoted as RS^ (or simply R^ for short).

Example 6: Suppose that the ontology has the following subsumption relation steals(Thief, TheftVictim)

� offends(Offender), then the second relation type could be extended to become: offends^(Offender, OffenceVictim), in which the second argument (OffenceVictim) of the relation supertype is a generalization (or a concept supertype) of the second argument (TheftVictim) of the relation subtype. The subsumption relation is still maintained for the new

relation type, i.e., steals(Thief, TheftVictim) �

offends^(Offender, OffenceVictim). It should also be noted that the new argument (OffenceVictim) should be

decided by a domain expert among the supertypes of TheftVictim in the concept type hierarchy, and should be added to that hierarchy if it was not there previously.

2.2.2 Instance Generalization The above argument generalization rule is complemented by the instance generalization rule (Nguyen et al. Dec. 2009), which applies to any (concept, relation or meta-relation) type and states that:

(1) ∀C,D∈TC ∀c∈C (C�D ⇒ ∃d∈D c�d)

(2) ∀S,R∈TR∪TMR ∀s∈S (S�R ⇒ ∃r∈R s�r and B(s) = B(r))

In simple terms, this means that: “Any subtype instance (including their properties) can be generalized into a supertype instance. In addition, in case of relations or meta-relations, these instances have the same arguments”.

By combining the above two rules (Sect. 2.2.1 and

2.2.2), it can be deduced that: Arguments of a subtype instance can be generalized into the corresponding arguments of a supertype instance (Extended Type Argument Generalization).

Example 7: Suppose that the ontology contains the

subsumption relation steals(Thief, TheftVictim) �

offends(Offender, OffenceVictim, OffenceMotive) and the instance John steals $5 from Mary. That instance could be written as steals(Thief:John, TheftVictim:Mary, <StolenObject:$5>). The generalization of that instance into an instance of the relation type offends could be written as offends(Offender:John, OffenceVictim:Mary, OffenceMotive:$5), translated as John commits an offence against Mary with $5 as a motive. If offends only has the first two arguments, then the generalization should be written as offends(Offender:John, OffenceVictim:Mary, <OffenceMotive:$5>). Note that it can be seen later that inferencing is easier through type closures and it is better for the above relation types to first be extended to have the same number of arguments.

2.2.3 Type Inheritance and Specialization

The type inheritance or specialization rule (Nguyen et al. Dec. 2009) applies to all types (concept, relation and meta-relation) where relevant, and states that:

(1) ∀U∈T ∀u∈U (u can inherit arguments and properties of U)

(2) ∀U,V∈T (U�V ⇒ U can specialize arguments and properties of V)

Or, in simple terms, “Arguments and properties of a type can be inherited by its instances and specialized by its subtypes”. Note that in this operation, the supertype arguments are merged with the semantics of the subtype to become the proper arguments of the latter, i.e., they are specialized by the subtype (see also Example 9), while inheritance means that arguments are properties are carried over as is.

This rule could be split into four separate rules: - Arguments of a subtype can be extended to be

subsumed into the corresponding arguments of the supertype (Type Argument Specialization).

- Supertype properties can be inherited by subtype (Type Properties Inheritance).

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- Type arguments can be inherited by type instance (Instance Inheritance of Type Arguments).

- Type properties can be inherited by type instance (Instance Inheritance of Type Properties).

See Sect. 3 for more formal properties of this rule. By applying this rule recursively, it can also be

deduced that: - Arguments and properties of a type can be inherited

and specialized by a subtype instance (Recursive Type Inheritance and Specialization).

- Properties of arguments of a type can be inherited by a subtype instance (Extended Recursive Type Inheritance and Specialization).

Example 8: As murder is pre-meditated human

killing, the subsumption relation murders � kills could be assumed. Suppose that the ontology contains the relation type murders(Murderer), the relation type kills(Killer, Victim, <minimumJailTerm: 1year>) (which translates a law stating that any homicide carries a minimum sentence of one-year jail term), and an instance John is a murderer (which can be written as murders(Murderer:John)), then the following new instance could be inferred murders(Murderer:John, MurderVictim, <minimumJailTerm: 1year>), i.e., John commits a murder against an unknown victim and is to be sentenced to at least one year in jail, in which the property minimimJailTerm of the supertype kills is inherited by the instance of the subtype murders. As noted previously, it can be seen later that inferencing is easier through relation type closures, which ensure that the above relation types are extended to have the same number of arguments.

2.2.4 Type Closure For a relation or meta-relation type, the type argument generalization and the type inheritance rules could be recursively applied with respect to each of its subtypes and supertypes, until its tuple of arguments becomes no longer extendable. The new relation or meta-relation type is then said to be closed and written with a superscript “*” after the type label. The type hierarchy in which all types are replaced by their closures is called the closure of the initial type hierarchy.

By definition, two types are said to be related if there is a path of subsumption relations in the type hierarchy from one type to the other type without ever going through the Top nor Bottom type. The closure of a type in essence incorporates into the type the relevant semantics of its related types, or enhances the type’s semantics with that of its related types.

The closure of the relation (or meta-relation) type hierarchy is obtained through recursive application of the following operations: (1) For each type in the hierarchy, its arguments

generalize the arguments of its subtypes. This is a recursive application of the Type Argument Generalization rule with respect to each of the subtypes.

(2) For each type in the hierarchy, its arguments and properties inherit the arguments and properties of its supertypes. This is a recursive application of the Type Argument Inheritance rule with respect to each

of its supertypes. See Sect. 3 for more formal properties of type closure.

Example 9: Suppose that the ontology contains three relation types picksPocket(PettyLarcenist, PickpocketVictim, StolenAmount), steals(Thief) and offends(Offender, OffenceVictim, OffenceAct, OffenceInstrument) and two subsumption relations

between them picksPocket � steals � offends. The closure of the relation type steals would be: steals*(Thief, TheftVictim, OffenceAct:Stealing, OffenceInstrument, StolenObject). In this new relation type, three arguments from the supertype offends are inherited (and specialized with the semantics of the relation type steals), e.g., OffenceVictim is inherited and merged with the semantics of steals to become TheftVictim, and one argument from the subtype picksPocket is generalized (from StolenAmount to StolenObject). Note that as mentioned previously, these new argument labels, when added to the ontology for the first time, need to be selected by a domain expert.

2.2.5 Rule Summary Table 1 is a summary of all rules that apply to the ontology formalism proposed in this paper. Rule Name Short Description Reference

Conformance Rule Unique infimum for any two types

Sect.2.1.2(3)

B-rule Consistency between relation type subsumption and relation type argument subsumption

Sect.2.1.2(5)

Type Argument Generalization (+)

Generalization of subtype argument into supertype argument

Sect.2.2.1

Instance Generalization (+++)

Generalization of subtype instance into supertype instance

Sect.2.2.2

Extended Type Argument Generalization (++)

Generalization of subtype instance argument into supertype instance argument

Sect.2.2.2

Type Inheritance and Specialization (*)

Inheritance of type arguments and type properties by type instances and subtypes

Sect.2.2.3

Type Argument Specialization

Extension of subtype argument tuple to be subsumed into supertype argument tuple

Sect.2.2.3

Recursive Type Inheritance and Specialization (**)

Inheritance of type arguments and type properties by subtype instance

Sect.2.2.3

Extended Recursive Type Inheritance and Specialization (***)

Inheritance of type argument properties by subtype instance

Sect.2.2.3

Type Label Uniqueness

Uniqueness of type labels (removal of type synonyms)

Sect.2.1.2(1)

Argument Label Uniqueness

Uniqueness of argument labels (removal of argument synonyms)

Sect.2.1.2(2)

Argument Tuple Consistency

Consistency in argument tuple listing orders between subtype and supertype

Sect.2.1.2(6)

Subsumption Cyclic Consistency Check

Removal of cyclic subsumption relations in the hierarchy (depending on upper ontology used)

Sect.2.1.2(7)

Table 1. Summary of ontological rules

Note that rule (*) can also be split into 4 different rules (as per Sect. 2.2.3).

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With regard to argument propagation between relation and meta-relation types, Table 2 summarizes the rules of propagation of instances, arguments and properties in an ontology. The way to read the table is to start with the row heading, then the displayed rule, and finally the column heading, e.g., “concept type properties (row heading) are inherited (rule *) by subtype (column heading)”, “relation or meta-relation type arguments (row heading) are generalized (rule +) into supertype (column heading)”, “relation or meta-relation instance (row heading) is generalized (rule +++) into supertype instance (column heading)”, etc. Note that the rules do not apply to the Top and Bottom types (as they are fictitious).

Subtype Supertype Instance Subtype

instance Supertype instance

Concept type properties

Inherited (*)

- Inherited (*)

Inherited (**) -

Concept instance

- - - - Generalized (+++)

Concept instance properties

- - - - Generalized (+++)

Relation or meta-relation type arguments

Specialized (*)

Generalized (+)

Specialized (*)

Specialized (**)

Generalized (++)

Relation or meta-relation type properties

Inherited (*)

- Inherited (*)

Inherited (**) -

Relation or meta-relation instance

- - - - Generalized (+++)

Relation or meta-relation instance arguments

- - - - Generalized (+++)

Relation or meta-relation instance properties

- - - - Generalized (+++)

Relation or meta-relation type argument properties

Inherited (*)

- Inherited (*)

Inherited (***)

-

Table 2. Summary of rules of propagation (with references to rules indicated in Column 1 of Table 1)

2.3 Non-Inferencing Rules

In Table 2, cells marked with a dash “-” are where there is no propagation rule identified. This is also the case when there is no cell representing a linkage between two ontological objects or attributes (e.g., between “concept instance properties” and “concept type properties”). These non-propagation rules include the notable rules listed below.

2.3.1 Non-Generalization of Type Properties

Properties of a subtype are not generalized into a supertype, only their arguments are. In Example 6, if, in addition, stealing is governed by the Theft Act 1968, then a new property could be added to steals, i.e., the relation type could be written as steals(Thief, TheftVictim, <underTheftAct1968>), but it cannot be generalized into

the supertype offends, i.e., not any offence can be considered under the Theft Act 1968.

2.3.2 Non-Generalization of Type Argument

Properties

Similarly, properties of an argument of a subtype cannot be generalized into properties of a subsuming argument of a supertype. For example, if by definition of a theft, a theft victim does not sustain physical injury during the theft, then <noPhysicalInjury> could be written as a property of the concept type TheftVictim. But this property cannot be generalized into a property of the subsuming argument OffenceVictim of the supertype offends.

2.3.3 Non-Generalization of Instance

Properties into Type Properties

Instance properties inherit from type properties (Type Inheritance rule) but not the other way around. In Example 7, the property <StolenObject:$5> of the instance steals (Thief:John, TheftVictim:Mary, <StolenObject:$5>) cannot be generalized into the type steals (Thief, TheftVictim, <StolenObject:$5>) (which means that any theft would involve $5).

2.3.4 Non-Inheritance of Instance Properties

by Subtype Instance

Instance properties could be generalized into supertype instance properties or arguments (Instance Generalization rule) but not the other way around. In Example 7, if it is initially known that “John commits an offence against Mary over $5 as the motive”, i.e., offends(Offender:John, OffenceVictim:Mary, <OffenceMotive:$5>), then it cannot be deduced that “John steals $5 from Mary”.

2.3.5 Rule Summary

Table 3 summarizes notable non-propagation rules.

Rule Name Short Description Reference

Non-Generalization of Type Properties into Supertype Properties

Subtype properties are NOT generalized into supertype properties (but subtype properties inherit from supertype properties)

Sect.2.3.1

Non-Generalization of Type Argument Properties into Supertype Argument Properties

Subtype argument properties are NOT generalized into supertype argument properties (but subtype argument properties inherit from supertype argument properties)

Sect.2.3.2

Non-Generalization of Instance Properties into Type Properties

Instance properties are NOT generalized (nor inherited) by type properties (but instance properties inherit from type properties)

Sect.2.3.3

Non-Inheritance of Instance Properties by Subtype Instance

Instance properties are NOT inherited by a subtype instance (but instance properties can be generalized into a supertype instance)

Sect.2.3.4

Table 3. Notable non-propagation rules

3 Mathematical properties of Proposed

Ontology Formalism

This section summarizes and enhances the mathematical properties of the proposed ontology formalism (Nguyen

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and Corbett Feb./Aug. 2006, Nguyen et al. 2008, Oct./Dec. 2009).

Definition 5 (Subsumption Sets). To facilitate later maintenance of the ontology, for every type t in the ontology, four sets of types (called subsumption sets of t) are kept up-to-date: the set of all its supertypes (denoted as super(t)), the set of all its immediate supertypes (denoted as isuper(t)), the set of all its subtypes (denoted as sub(t)), and the set of all its immediate subtypes (denoted as isub(t)). By extension, the subsumption sets of a set of types and the combinations of subsumption operations on a type are also defined as per normal conventions, e.g.,

- sub(S) denotes the set of all subtypes of all types in S,

i.e., sub(S) = ∪t∈S sub(t). - sub(isub(t)) denotes the set of all subtypes of all

immediate subtypes of t, i.e., sub(isub(t)) = ∪u∈isub(t) sub(u).

Proposition 1 (Subsumption Redundancy): A new

subsumption relation u�t is redundant in the ontology if

and only if u∈sub(isub(t)). Proof. If there are no existing immediate subtypes of t

(different from u), i.e., isub(t)=∅, then the proposition is proven. If there are, and if there exists an immediate

subtype t” of t (i.e., t”∈isub(t)) such that u belongs to

sub(t”) (or u∈sub(isub(t))) then u�t is a redundant subsumption relation by definition.

Proposition 2 (Subsumption Conformance): A new

non-redundant subsumption relation u�t breaks the

conformance rule if u∈isub(isuper(isub(t))). Proof. Breaking the conformance rule means causing

the type hierarchy not to be a semi-lattice, or having a pair of types with more than one immediate common subtype. If there are no existing immediate subtypes of t

different from u, then the new subsumption relation u�t could be added to the ontology without breaking the conformance rule. If there is at least one such type t”

(i.e., t”∈isub(t)), consider all immediate supertypes of t”

and if there exists such a supertype t’ (i.e., t’∈isuper(t”))

such that u belongs to isub(t’) (or u∈isub(isuper(isub(t)))) then both u and t” are infima of t and t’ and therefore the hierarchy would not be a semi-lattice if the new subsumption relation is added. Fig. 1 shows the example of a non-semi-lattice structure and Fig. 2 shows how the semi-lattice structure is restored by adding a new intermediate type.

Definition 6 (Tuple Extension and Subsumption):

(1) Tuple definition: Given a set X, a tuple over X is

defined as a member of the set τ(X) = ∪{n>0}(X)n. The set of all type tuples is denoted as Г.

(2) Tuple membership: A component e of a tuple T is

written as e∈T (the notation “∈”, normally reserved for set membership, is extended to tuple components).

(3) Tuple extension: Let T1=<e1, …, en> be an n-tuple and T2=<f1, …, fm> be an m-tuple, T1 is said to be an extension of T2 (or T1 is said to extend T2), and

written as T1=ext(T2) or T2 ⊆ T1 (or T2 ⊂ T1 for a

strict extension), if all components of T2 are also present in T1 with their relative listing order

respected, i.e., T1=ext(T2) ⇔ <e1, …, en>= ext(<f1,

…, fm>) ⇔ (m ≤ n) and (∀k,l 1 ≤ k ≤ l ≤ m ∃i,j with

1 ≤ i ≤ j ≤ n and ei = fk and ej = fl) (4) Type tuple subsumption: Let T1 and T2 be an n-tuple

and m-tuple of types respectively with m ≤ n. T1 is

said to subsume T2 (and we write T2 � T1) if there exists an m-tuple T2’ of types such that: - T1=ext(T2’) and - Each component of T2 is subsumed into the corresponding component of T2’, i.e., if T2 = <f1, …,

fm> and T2’ = < fi’, …, fm’> then ∀i 1 ≤ i ≤ m fi � fi’ Note that with the above definition the subsumption relation is extended from subsumption between two types to subsumption between two tuples of types.

Example10 (Type Tuple Subsumption): Let T1 = <Person, LivingEntity, Person> and T2 = <Woman,

Animal>. The tuple subsumption relation: T2�T1 is true because T2’ = <Person, LivingEntity> fulfills the tuple subsumption conditions with: - T1 = ext(T2’)

- Woman � Person (i.e., 1st argument of T2 � 1st argument of T2’)

- Animal � LivingEntity (i.e., 2nd argument of T2 �

2nd argument of T2’)

Proposition 3 (Tuple Extension and Subsumption

Properties): It could be easily proven that the type tuple

extension relation is: (∀T1 ,T2,T3 ∈ Г) (1) reflexive, i.e., T1=ext(T1)

(2) anti-symmetrical, i.e., T1=ext(T2) and T2=ext(T1) ⇒ T1=T2

(3) subsuming, i.e., T1=ext(T2) ⇒ T2 � T1

(4) transitive, i.e., T1=ext(T2) and T2=ext(T3) ⇒ T1=ext(T3)

(5) subsumingly transitive, i.e., T1 � T2 and T3=ext(T2) ⇒

T1 � T3

(6) transitively subsuming, i.e., T2=ext(T1) and T2 � T3 ⇒

T1 � T3 Prop. 4 can be easily deduced from the Type

Argument Generalization rule (Sect 2.2.1).

Proposition 4 (Type Argument Generalization properties): Let S and R be two relation (or meta-

relation) types with S � R, then there is a relation (or

Fig. 1. Example of non-semi-lattice

kidnapsWith

Ransom

assaults robs

carJacks kidnapsWith

Ransom

robsWithViolence

assaults robs

carJacks

Fig. 2. Example of semi-lattice restored

68

meta-relation) type, called an upward extension of R with respect to S and denoted as RS^ (or simply R^ when there is no ambiguity), such that: (1) R^ ≡ R (2) B(R^) = ext(B(R))

(3) B(S) � B(R^) The above upward extension can also be defined as a

partial function:

Λ: (TR∪TMR) x (TR∪TMR) → TR∪TMR with

∀R∈TR∪TMR ∀S∈sub(R) Λ(S,R) = RS^

Note that Statement b) implies that B(R) � B(R^) (as per Proposition 1(3)). If all upward extensions of a type are added to the ontology, then it can be deduced that

semantically S � R = R^ but syntactically S � R � R^ (see Sect. 2.1(7) for syntactical subsumption).

Prop. 5 can be easily deduced from the Type

Argument Inheritance rule (Sect 2.2.3), similarly to the Type Argument Generalization rule.

Proposition 5 (Type Argument Specialization properties): Let S and R be two relation (or meta-

relation) types with S � R, then there is a relation (or meta-relation) type, called an downward extension of S with respect to R and denoted as SR

V (or simply SV when there is no ambiguity), such that: (1) SV ≡ S (2) B(SV) = ext(B(S))

(3) B(SV) � B(R^) The above downward extension can also be defined as

a partial function:

V: (TR∪TMR) x (TR∪TMR) → TR∪TMR with

∀S∈TR∪TMR ∀R∈super(S) V(S,R) = SRV

Note that Statement c) is slightly different from the corresponding Statement in the previous rule since tuple subsumption requires that the subsuming tuple has more components than the subsumed tuple. If all downward extensions of a type are added to the ontology, then it can

also be deduced that semantically S = SV� R = R^ but

syntactically S � SV� R^ .

Relation and Meta-relation Type Closure:

The closure (Sect. 2.2.4) of a relation or meta-relation type R (denoted as R*) is mathematically defined as the recursive application of the Type Argument Generalization and Inheritance rules to R until that application becomes idempotent.

Propositions 6, 7 and 9 below could be easily proven from the closure definition.

Proposition 6 (Hierarchy Closure Determination):

(1) For a type or a hierarchy of types, the closure operation is idempotent. (2) The closures of all related types in a hierarchy have the same arity (i.e., same number of arguments), with each argument of a supertype subsuming a corresponding argument of a subtype.

Proposition 7 (Hierarchy Closure Determination): A

type hierarchy H is closed if and only if: ∀R∈H

(∀W∈super(R) V(R,W)=R) and (∀S∈sub(R) Λ(S,R)=R)

Definition 7 (Type Closure): The hierarchy closure is obtained by repeating an operation called “sweep”, until the resulting hierarchy is stable, i.e., until the total number of all arguments of all types in the hierarchy (where each argument is counted separately) is stable. A “sweep” is defined as the process of replacing each type R and U in the hierarchy with its extension R^ and U^ defined as follows:

∀U∈isub(T)

U^ = П Λ(S,U) (Eq. 1)

S∈sub(U)

∀R∈sub(U^) R^ = V(R,U^) (Eq. 2) The “closure index” is defined as the number of

sweeps required to achieve the hierarchy closure. This helps determine the mathematical complexity of the implementation of type hierarchy closure (e.g., given a type hierarchy, how long does the implementation of this algorithm have to run in order to produce the closure of that type hierarchy?).

Note that in the above: - Eq. 1 defines, for any highest type U different from the Top type (T), its extension U^, which is obtained by propagating (upwards) to U all the arguments of all subtypes of U. - Eq. 2 defines, for any subtype R of a highest type U^ obtained as above, its extension R^, which is obtained by propagating (downwards) to R all the arguments of U^.

Proposition 8 (Closure Index Determination): The closure index is bounded by (a-1)/2, with a being the total number of relation types in the hierarchy (excluding the fictitious Top and Bottom types).

Proof. For an argument to be propagated from one relation type to another relation type, the maximum number of “hops” that it needs to take is bounded by (a-1) as in the worst case it needs to propagated to all other relation types before reaching the destination type, i.e., it needs to go through a maximum of (a-1) relation types. In addition, each sweep allows the argument being considered to reach at least 2 new relation types (as a sweep must go up and down the hierarchy). Thus the number of sweeps to achieve closure of the hierarchy (i.e., the closure index) is bounded by (a-1)/2.

Example 11: Consider a simple relation type hierarchy with 3 types: assaults(Assaulter), kidnaps(KidnapVictim), carjacks(CarjackWitness), and 2 subsumptions: kidnaps()

� assaults(), and carjacks() ≼ assaults(). First, as per Table 2, the argument of assaults could be propagated the relation type kidnaps, i.e., its extended type is kidnaps^(Kidnapper, KidnapVictim). However, assaults is the supertype of both kidnaps and carjacks, and therefore the arguments of these two subtypes could be generalized into assaults. Its extended type would now become assaults^(Assaulter, AssaultVictim, AssaultWitness). For the relation type kidnaps to be complete, a second application of Table 2 would be necessary in order for it to inherit the latest set of

69

arguments of assaults. The closure of the relation type kidnaps would now have three arguments: kidnaps*(Kidnapper, KidnapVictim, KidnapWitness). The closures of the other 2 relation types are also determined similarly (See Fig. 3 and 4).

Moreover, suppose that the above ontology also

contains the relation type robs(Robber, RobbedProperty) as a supertype of carjacks(CarjackWitness). In this case the new argument of robs, which is RobbedProperty, would propagate to its subtype carjacks, then from there, to assaults and kidnaps (Fig. 5 and 6). This means that the arguments of a relation type closure are impacted by those of all of its related types, like a ripple effect.

4 Conclusion This paper presented a detailed list of inferencing rules and operations concerning an ontology formalism previously proposed for Conceptual Structure Theory. The ontology could be constructed for any domain, business sector or application. The process of creating the ontology as well as of applying the inferencing rules are provided to assist with real-life implementation of the proposed formalism. Since ontologies are the core of the future semantic web, the proposed method could serve as the blue print for future implementation of a variety of

semantic inferencing applications, including semantic search engines, semantic query-answering systems, etc.

5 References

Kaneiwa K., “Order-sorted logic programming with predicate hierarchy”, Artificial Intelligence, Vol. 158, No. 2, pp. 155-188, 2004.

Kaneiwa K., Iwazume M. and Fukuda K., “An Upper Ontology for Event Classifications and Relations”, 20th Australian Joint Conference on Artificial Intelligence, Dec. 2007, Gold Coast, Australia, LNCS, Vol. 4830, pp. 394-403.

Kaneiwa K. and Nguyen P., “Decidable Order-Sorted Logic Programming for Ontologies and Rules with Argument Restructuring”, 8th international semantic web conference, Washington, DC, USA, LNCS 5823:328-343, Oct. 2009.

Kingston J., Schafer B. and Vandenberghe W., “Towards a Financial Fraud Ontology: A Legal Modelling Approach”, Artificial Intelligence and Law, 12:4, pp. 419-446, 2004.

Horrocks I. and Patel-Schneider P., “Optimising Description Logic Subsumption”, Journal of Logic and Computation, 9:3, pp. 267-293, 1999.

Nguyen P. and Corbett D., “A Basic Mathematical Framework for Conceptual Graphs,” IEEE Transaction on Knowledge and Data Engineering, Vol. 18, No. 2, pp. 261-271, Feb. 2006.

Nguyen P. and Corbett D., “Building Corporate Knowledge through Ontology Integration”, Pacific Rim Knowledge Acquisition Workshop (PKAW-06), Aug. 2006, Guilin, China, LNAI 4303, pp. 223-229.

Nguyen P., Kaneiwa K., Corbett D. and Nguyen M.Q., “An Ontology Formalization of Relation Type Hierarchy in Conceptual Structure Theory”, 21st Australasian Conf. on AI, Auckland, NZ, Dec. 2008, LNAI 5360 - pp 79-85.

Nguyen P., Kaneiwa K., Corbett D. and Nguyen M.Q., “Representing Event Assertions in an Upper Event Ontology”, Proc. First International Conference on Knowledge and System Engineering (KSE-2009), Hanoi, Vietnam, 13-17 Oct 2009, pp. 120-125.

Nguyen P., Kaneiwa K., Corbett D. and Nguyen M.Q., “Meta-relation and ontology closure in Conceptual Structure Theory”, Artificial Intelligence and Law, 17:4:291-320, Dec 2009.

Sowa J., “Knowledge Representation: Logical, Philosophical, and Computational Foundations”, Brooks Cole Publishing Co., Pacific Grove, CA, 2000.

Stumme G., “Using Ontologies and Formal Concept Analysis for Organizing Business Knowledge”, in “Wissensmanagement mit Referenzmodellen - Konzepte für die Anwendungssystem und Organisationsgestaltung”, J. Becker, R. Knackstedt (Eds.), pp. 163-174, 2002.

Wille R., “Restructuring lattice theory: an approach based on hierarchies of concepts”, in “Ordered Sets”, I. Rival (ed.), Reidel, Dordrecht-Boston, 1982.

kidnaps

(KidnapVictim)

carjacks (CarjackWitness)

assaults

(Assaulter)

robs (Robber,

RobbedProperty)

Fig. 5. Ontology with 4 relation types (before application of relation type closure)

kidnaps*(Kidnapper, KidnapVictim, KidnapWitness,

KidnapMotive)

carjacks*(Carjacker, CarjackVictim, CarjackWitness,

RobbedProperty:Car)

assaults*(Assaulter, AssaultVictim, AssaultWitnesss,

AssaultMotive)

Fig. 6. Ontology with 4 relation types (after application of relation type closure)

robs*(Robber, RobberyVictim, RobberyWitnesss, RobbedProperty)

kidnaps (KidnapVictim)

carjacks (CarjackWitness)

assaults (Assaulter)

Fig. 3. Ontology with 3 relation types (before application of relation type closure)

kidnaps*(Kidnapper, KidnapVictim,

KidnapWitness)

carjacks*(Carjacker, CarjackVictim,

CarjackWitness)

assaults*(Assaulter, AssaultVictim, AssaultWitnesss)

Fig. 4. Ontology with 3 relation types (after application of relation type closure)

70

An Axiomatisation of Basic Formal Ontology with ProjectionFunctions

Kerry Trentelman1 Alan Ruttenberg2,3 Barry Smith1

1National Center for Biomedical Ontology,New York State Center of Excellence in Bioinformatics and Life Sciences,

State University of New York at BuffaloEmail: {kerrytre,phismith}@buffalo.edu

2School of Dental Medicine,State University of New York at Buffalo

3Creative CommonsEmail: alanruttenberg@gmail.com

Abstract

This paper proposes a reformulation of the treatmentof boundaries, fiat parts and aggregates of entities inBasic Formal Ontology. These are currently treatedas mutually exclusive, which is inadequate for biolog-ical representation since some entities may simulta-neously be fiat parts, boundaries and/or aggregates.We introduce functions which map entities to theirboundaries, fiat parts or aggregations. We make useof time, space and spacetime projection functionswhich, along the way, allow us to develop a simpletemporal theory.

Keywords: ontology, mereology, axiomatisation

1 Introduction

Developed at the Institute for Formal Ontology andMedical Information Science, Basic Formal Ontology(BFO) is a theory of the basic structures of reality.BFO endorses the view that the world contains occur-rents and continuants. Occurrents are entities whichunfold, or develop in time. Continuants are entitieswhich have a continuous existence and a capacity toendure through time. Both types of entities existin time in different ways. By heeding a notion of(Zemach 1970), namely that distinct modes of beinggenerate distinct ontologies, BFO distinguishes be-tween two kinds of ontologies: one for continuants,the other for occurrents. The Open Biomedical On-tologies consortium’s Relation Ontology describes in-ter and intra relations between the two ontologies inorder to support automated reasoning about the spa-tiotemporal, temporal and spatial dimensions of bi-ological and medical phenomena. We refer to BFOmerged with the Relation Ontology simply as ‘BFO’.

This work was funded by the National Institute of Healththrough the NIH Roadmap for Medical Research, Grant 1 U54 HG004028.

Copyright c©2010, Australian Computer Society, Inc. This pa-per appeared at the Sixth Australasian Ontology WorkshopAOW 2010), Adelaide, Australia. Conferences in Researchand Practice in Information Technology (CRPIT), Vol. 122,Thomas Meyer and Mehmet A. Orgun and Kerry Taylor, Ed.Reproduction for academic, not-for-profit purposes permittedprovided this text is included.

In BFO there are three main categories of occur-rents: processes, spatiotemporal regions and tempo-ral regions. Examples of processes include the processof respiration, a human life, the development of anembryo, the flight of a bird, and the functioning of theheart. Examples of spatiotemporal regions includethe spatiotemporal location of an individual organ-ism’s life and the spatiotemporal location of a repli-cating strand of DNA, whereas examples of temporalregions include the time taken by a cell undergoingmeiosis, and the moment a finger is detached in anindustrial accident. In BFO there are three main cat-egories of continuants: dependent continuants, inde-pendent continuants and spatial regions. Dependentcontinuants are entities such as qualities, roles anddispositions that inhere in independent continuants.Independent continuants are entities in which depen-dent continuants, such as qualities and dispositionscan inhere in. Examples of independent continuantsinclude a human individual and a heart, whereas ex-amples of dependent continuants include the mass ofa cloud, the role of being a doctor, the disposition of avase to break when dropped, the function of the heartto pump blood and the spectrum of the sun. Exam-ples of spatial regions include a cubed-shape part ofspace, and a point in space.

The paper is structured as follows. Section 2 pro-vides an overview of the BFO type hierarchy and isbased on work found in (Spear 2006). Sections 3 and4 describe mereological relations which are requiredin later sections. Section 3 is influenced by theorydescribed by (Simons 1987), whereas Section 4 is in-fluenced by (Smith 1996). Section 5.2 is based onwork in (Smith et al. 2005), however the rest of Sec-tion 5 is new material. Here we introduce our time,space and spacetime projection functions and outlinea simple temporal theory. Section 6 is entirely newand introduces functions which handle boundaries,fiat parts and aggregates. Section 7 draws conclu-sions. Throughout this paper we rely on the typog-raphy described in Figure 1. Relations between typesare depicted in italics, whereas all other relations aredepicted in bold. The logical connectors ¬, =, ∧, ∨,⇒ and⇔ have their usual interpretation. The symbol=def is used for definitions, ∀ for universal quantifi-cation, ∃ for existential quantification, and ι for thedefinite descriptor. We omit leading universal quan-tifiers in our formulae. Names of axioms begin with‘A’, names of definitions begin with ‘D’, and namesof theorems begin with ‘T’.

71

Occurrent O oProcess P pSpatiotemporal Region U uScattered Spatiotemporal Region us(k)

Connected Spatiotemporal Region uc

Temporal Region T tScattered Temporal Region ts(k)

Connected Temporal Region tc

Temporal Instant iTemporal Interval v

Continuant C cSpatial Region S sIndependent Continuant A aMaterial Continuant M mSite

Dependent ContinuantGeneric Dependent ContinuantSpecific Dependent ContinuantQualityRealisable EntityRoleDispositionFunction

time projection τspace projection ψ, ψi

spacetime projection µboundary function β, βi

fiat part function ϕ, ϕi

aggregation function α, αi

Figure 1: Candidate BFO 2.0 type hierarchy and ty-pography used throughout this paper. Upper-case ro-man letters denote occurrent and continuant typesand lower-case roman letters denote instances.

2 The type hierarchy

BFO distinguishes between types and instances.Types are what all members of a natural kind, group-ing or species have in common. For example: cat,cell and photosynthesis are types. Instances can bethought of as the individual occupants of reality. Forexample: my neighbour’s cat, the red blood cell onthis microscope slide, and the process of photosynthe-sis the gum tree in my backyard performs throughoutits lifetime are all instances. Types can be instanti-ated by more than one entity at more than one time,whereas instances are one-off, they can exist only inone place at one time. Types exist when and wheretheir instantiations exist. Instances exist in space andtime, and come into and pass out of existence.

2.1 Instances and subtypes

The primitive binary relational assertionx instance of X has the meaning: instance xis an instantiation of type X. We say ‘x is an occur-rent instance’ (or, more simply, ‘x is an occurrent’) ifand only if x instance of Occurrent . A type X is asubtype of Occurrent if and only if all instances of Xare occurrents. In that case we call X an ‘occurrenttype’. In the following we use O, O1, . . . and o, o1, . . .to range over occurrent types and occurrents, respec-tively. In BFO, an example of an occurrent type is

Temporal Instant . We say “x is a temporal instantinstance’ (or, more simply, x is a ‘temporal instant’)if and only if x instance of Temporal Instant . Weuse i, i1, . . . to range over temporal instants.

The primitive ternary relational assertionx instance ofX at i has the meaning: instance x isan instantiation of type X at the temporal instanti. We say ‘x is a continuant instance at temporalinstant i’ (or, more simply ‘x is a continuant at i’) ifand only if x instance of Continuant at i. A type Xis a subtype of Continuant if and only if all instancesof X at any temporal instant are continuants atthat instant. In that case we call X a ‘continuanttype’. We use C, C1, . . . and c, c1, . . . to range overcontinuant types and continuants. We furthermorewrite o :O as an abbreviation for o instance ofO andc :C at i as an abbreviation for c instance of C at i.

Any two occurrent types are such that the in-stances of one are not the instances of the other.Any two continuants types are such that the instancesof one at any given temporal instant are not the in-stances of the other at that same temporal instant.

O1 = O2 ⇒ ∀o. (o :O1 ⇔ o :O2) (A2.1)C1 = C2 ⇒ ∀c, i. (c :C1 at i⇔ c :C2 at i) (A2.2)

An occurrent type O1 is a (subtype of) occurrenttype O2 if and only if all instances of O1 are alsoinstances of O2. A continuant type C1 is a continu-ant type C2 if and only if all instances of C1 at anytemporal instant i are also instances of C2 at i.

O1 is a O2 =def ∀o. o :O1 ⇒ o :O2 (D2.1)C1 is a C2 =def ∀c, i. c :C1 at i⇒ c :C2 at i (D2.2)

For example: DNA is a nucleic acid ;photosynthesis is a physiological process.

Although we do not show them here, using defin-tions D2.1 and D2.2, and axioms A2.1 and A2.2, wecan prove theorems which state that the subtype rela-tion is reflexive, antisymmetric and transitive. More-over we can trivially prove two theorems (that appearin later proofs) which tell us that occurrent and con-tinuant types inherit their subtype instances.

o :O1 ∧O1 is a O2 ⇒ o :O2 (T2.1)c :C1 at i ∧ C1 is a C2 ⇒ c :C2 at i (T2.2)

2.2 Occurrent types

Occurrents are entities that happen, unfold, ordevelop in time. They are sometimes referredto as ‘perdurant’ entities. The type Occurrenthas three mutually exclusive subclasses: Process,Spatiotemporal Region and Temporal Region. Pro-cesses always depend on one or more independentcontinuants. For example the flight of a bird, thelife of an organism, the process of cell division, or thecourse of a disease.

Process is a Occurrent (A2.3)Spatiotemporal Region is a Occurrent (A2.4)

Temporal Region is a Occurrent (A2.5)

We differentiate between connected and scatteredspatiotemporal regions. A scattered spatiotemporalregion is the mereological sum of multiple connectedspatiotemporal regions which are separated in space-time. A connected spatiotemporal region is any spa-tiotemporal region that is not scattered.

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Scattered Spatiotemporal Region (A2.6)is a Spatiotemporal Region

Connected Spatiotemporal Region (A2.7)is a Spatiotemporal Region

A spatiotemporal interval is a connected spa-tiotemporal region that endures for more than a sin-gle instant of time. A spatiotemporal instant is aconnected spatiotemporal region at a specific instantin time.

Spatiotemporal Interval (A2.8)is a Connected Spatiotemporal Region

Spatiotemporal Instant (A2.9)is a Connected Spatiotemporal Region

We also differentiate between connected and scat-tered temporal regions. A scattered temporal regionis the mereological sum of multiple connected tempo-ral regions which are separate in time. A connectedtemporal region is any temporal region that is notscattered.

Connected Temporal Region (A2.10)is a Temporal Region

Scattered Temporal Region (A2.11)is a Temporal Region

A temporal interval is a connected temporal re-gion that lasts for more than a single instant of time.A temporal instant is a connected temporal regioncomprising a single instant in time.

Temporal Interval (A2.12)is a Connected Temporal Region

Temporal Instant (A2.13)is a Connected Temporal Region

2.3 Continuant types

Continuants are entities that exists in full atany time at which they exist at all, persistthrough time while maintaining their identity,and have no temporal parts. They are some-times referred to as ‘endurant’ entities. Thetype Continuant has three mutually exclusive sub-classes: Spatial Region, Independent Continuant andDependent Continuant .

Spatial Region is a Continuant (A2.14)Independent Continuant is a Continuant (A2.15)

Dependent Continuant is a Continuant (A2.16)

Any point, line, surface or volume is an instanceof Spatial Region.

Material continuants are entities which are thebearers of dependent continuants. They are entitiesin which dependent continuants inhere. Material con-tinuants themselves cannot inhere in anything. Sites(such as hollows, cavities and tunnels) are entitieswhich can move through space and also can be occu-pied by material continuants.

Material Continuant (A2.17)is a Independent Continuant

Site is a Independent Continuant (A2.18)

Dependent continuants are entities which inherein independent continuants. Thus in order to exist,some independent continuant must also exist. De-pendent continuants can be either specific or generic.An existing specific dependent continuant inheres ina single, specific bearer, whereas an existing genericdependent continuant can inhere in multiple bearers.For example the redness of this apple is not identicalto the redness of that apple, but the pdf file in myinbox and on my desktop are identical. For each en-tity in which a generic dependent continuant inheresthere exists a ‘concretization’ of the generic depen-dent continuant which is itself specific.

Specific Dependent Continuant (A2.19)is a Dependent Continuant

Generic Dependent Continuant (A2.20)is a Dependent Continuant

Qualities (such as temperature, shape and mass)are entities which inhere in a specific bearer and aresuch that they are exhibited in full whenever they areborne. Realisable entities are entities which inhere ina specific bearer and are sometimes (not always) re-alised as processes. For example the role of being asurgeon may inhere in a person, but that role is notrealised when that person is away from work. Like-wise the disposition of a match to ignite is realisedwhen the match is struck and starts to burn.

Quality (A2.21)is a Specific Dependent Continuant

Realisable Entity (A2.22)is a Specific Dependent Continuant

We do not further address dependent continuantsin this paper. We instead refer the reader to (Arp &Smith 2008) for more details.

3 Basic mereological relations

3.1 Parthood

In BFO, occurrent parthood is specified using theprimitive binary relational assertion o1 part of o2. Atime-indexed version c1 part ofc2 at i is used for con-tinuants where i is a temporal instant. The instancelevel parthood relation is reflexive (A3.1 and A3.2),antisymmetric (A3.3 and A3.4) and transitive (A3.5and A3.6).

o part of o (A3.1)c part of c at i (A3.2)

o1 part of o2 ∧ o2 part of o1 ⇔ o1 = o2 (A3.3)c1 part of c2 at i ∧ c2 part of c1 at i (A3.4)

⇔ c1 = c2

o1 part of o2 ∧ o2 part of o3 (A3.5)⇒ o1 part of o3

c1 part of c2 at i ∧ c2 part of c3 at i (A3.6)⇒ c1 part of c3 at i

If a spatial region s1 is part of a spatial region s2at a given temporal instant, then s1 is part of s2 at alltimes. For example, at this instant in time the spatialregion occupied by Tokyo is part of the spatial regionoccupied by Japan, but that same spatial configura-tion held before Tokyo was even built (and will hold

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after the city is demolished by Godzilla). Instead ofthe ternary relational assertion s1 part of s2 at i wewrite the binary assertion s1 part of s2 without thetime-index.

An occurrent type O1 is part of occurrent type O2if and only if for all instances o1 of O1, there existsan instance o2 of O2 such that o1 is part of o2. Acontinuant type C1 is part of continuant type C2 ifand only if for all instances c1 of C1 at any temporalinstant i, there exists an instance c2 of C2 at i suchthat c1 is part of c2 at i.

O1 part of O2 =def ∀o1. o1 :O1 (D3.1)⇒ ∃o2. o2 :O2 ∧ o1 part of o2

C1 part of C2 =def ∀c1, i. c1 :C1 at i (D3.2)⇒ ∃c2. c2 :C2 at i ∧ c1 part of c2 at i

For example: nucleoplasm part of nucleus;gastrulation part of embryonic development . Notethe definitions make use of an ‘all-some’ structure.O1s in every case exist as parts of O2s, however O2smay exist without having O1s as parts. For example:menopause part of ageing

Although we do not show them here, using defini-tions D3.1 and D3.2, and the reflexivity and transi-tivity of the instance-level parthood relation, we canprove theorems stating that the type-level parthoodrelation is reflexive and transitive. We specify axiomswhich tell us that the relation is antisymmetric.

3.2 Overlaps

Another relation we use frequently in this paper isoverlaps. A spatiotemporal region u1 overlaps aspatiotemporal region u2 if and only if there exists aspatiotemporal region u which is both a part of u1 andu2. We define similar relations for temporal regionsand spatial regions (not shown here). An independentcontinuant a1 overlaps an independent continuant a2at a temporal instant i if and only if there exists anindependent continuant a which is both a part of a1and a2 at i.

u1 overlaps u2 =def (D3.3)∃u. u part of u1 ∧ u part of u2

a1 overlaps a2 at i =def (D3.4)∃a. a part of a1 at i ∧ a part of a2 at i

The instance-level overlap relation is reflexive,symmetric and intransitive.

u overlaps u (T3.1)a overlaps a at i (T3.2)

u1 overlaps u2 ⇒ u2 overlaps u1 (T3.3)a1 overlaps a2 at i⇒ a2 overlaps a1 at i (T3.4)

∃u1, u2, u3. ¬(u1 overlaps u2 (T3.5)∧ u2 overlaps u3 ⇒ u1 overlaps u3)∃a1, a2, a3. ¬(a1 overlaps a2 at i (T3.6)

∧ a2 overlaps a3 at i⇒ a1 overlaps a3 at i)

Proof. Since u is an occurrent by A2.4 and T2.1, wecan prove T3.1 by A3.1 and D3.3. Similarly sincea is a continaunt by A2.15 and T2.2, we can proveT3.2 by A3.2 and D3.4. T3.3 and T3.4 follow fromD3.3 and D3.4, respectively. In order to prove T3.5by contradiction we choose spatiotemporal regions u1,

u2 and u2 such that u1 overlaps u2, u2 overlaps u3and ¬(u1 overlaps u2). We prove T3.6 in a similarfashion. �

A spatiotemporal region type U1 overlaps a spa-tiotemporal region type U2 if and only if for all in-stances u1 of U1, there exists an instance u2 of U2such that u1 overlapsu2. We define similar relationsfor temporal region types and spatial regions types(not shown here). An independent continuant typeA1 overlaps an independent continuant type A2 if andonly if for all instances a1 of A1 at any temporal in-stant i, there exists an instance a2 of A2 at i suchthat a1 overlaps a2 at i.

U1 overlaps U2 =def ∀u1. u1 :U1 (D3.5)⇒ ∃u2. u2 :U2 ∧ u1 overlaps u2

A1 overlaps A2 =def ∀a1, i. a1 :A1 at i (D3.6)⇒ ∃a2. a2 :A2 at i ∧ a1 overlaps a2 at i

For example: cube overlaps cube face; nucleusoverlaps cell .

The type-level overlap relation is reflexive (T3.7and T3.8), symmetric between spatiotemporal re-gion types (A3.7), antisymmetric between indepen-dent continuant types (A3.8), and intransitive (A3.9and A3.10). Note that T3.7, A3.7 and A3.9 also holdfor temporal region types and spatial region types.It is possible that A1 in general overlaps A2 whileno analogous statement holds for A2 in relation toA1. For example, although uterine tract overlapsurogenital system, it is not the case in general thaturogenital system overlaps uterine tract .

U overlaps U (T3.7)A overlaps A (T3.8)

U1 overlaps U2 ⇒ U2 overlaps U1 (A3.7)A1 overlaps A2 ∧A2 overlaps A1 (A3.8)

⇒ A1 = A2

∃U1, U2, U3. ¬(U1 overlaps U2 (A3.9)∧ U2 overlaps U3 ⇒ U1 overlaps U3)

∃A1, A2, A3. ¬(A1 overlaps A2 (A3.10)∧A2 overlaps A3 ⇒ A1 overlaps A3)

Proof. T3.7 can be proved by D3.5 and T3.1. T3.8can be proved by D3.6 and T3.2. �

4 Connected and scattered regions

This section describes standard mereological rela-tions, for example as outlined in (Casati & Varzi1999) and (Smith 1996), which allow us to define con-nected and scattered spatiotemporal and temporal re-gions.

For every property or condition ϕ that is true of atleast one spatiotemporal region, there is a spatiotem-poral region consisting precisely of all the ϕers. Thisspatiotemporal region is called the spatiotemporal fu-sion of the ϕers and is denoted σu(ϕu). We definethe temporal fusion and spatial fusion of the ϕers ina similar fashion (not shown here).

σu(ϕu) =def ιu1∀u2. (u1 overlaps u2 (D4.1)⇔ ∃u. (ϕu ∧ u overlaps u2))

We call u1 +u2 the sum of spatiotemporal regionsu1 and u2, and define it as the spatiotemporal fusionof parts of u1 or u2. We define the sum of temporal

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regions and the sum of spatial regions in a similarfashion (not shown here).

u1 + u2 =def σu(u part of u1 (D4.2)∨ u part of u2)

We call u1−u2 the difference of spatiotemporal re-gion u1 from spatiotemporal region u2, and define itas the spatiotemporal fusion of parts of u1 which don’toverlap u2. We call u the complement of spatiotem-poral region u, and define it as the spatiotemporalfusion of spatiotemporal regions which don’t overlapu. We define the difference of temporal regions andthe difference of spatial regions, and the complementof both temporal and spatial regions in a similar fash-ion (not shown here).

u1 − u2 =def σu(u part of u1 (D4.3)∧ ¬(u overlaps u2))

u =def σu′(¬(u′ overlaps u)) (D4.4)

The spatiotemporal region u1 is aninterior part of the spatiotemporal region u2if and only if u1 is a non-equivalent (i.e. proper) partof u2 and any spatiotemporal region which partiallyoverlaps u1 also overlaps the difference of u2 fromu1. We define similar relations for temporal regionsand spatial regions (not shown here).

u1 interior part of u2 =def u1 part of u2 (D4.5)∧ u1 6= u2

∧ (∀u′. u′ overlaps u1 ∧ ¬(u′ part of u1)∧ ¬(u1 part of u′)

⇒ u′ overlaps (u2 − u1))

A spatiotemporal region u1 crosses a spatiotem-poral region u2 if and only if u1 overlaps both u2and its complement. A spatiotemporal region u1straddles a spatiotemporal region u2 if and only ifany spatiotemporal region for which u1 is an inte-rior part also crosses u2. We define similar relationsfor temporal regions and spatial regions (not shownhere).

u1 crosses u2 =def u1 overlaps u2 (D4.6)∧ u1 overlaps u2

u1 straddles u2 =def (D4.7)∀u. u1 interior part of u⇒ u crosses u2

A spatiotemporal region u′ is the boundary ofa spatiotemporal region u if and only if any partof u′ also straddles u. We call u the closure of aspatiotemporal region u and define it as the sum ofu and its boundaries. A spatiotemporal region u1is separate from a spatiotemporal region u2 if andonly if the closure of u1 does not overlap u2 and u1does not overlap the closure of u2. We define similarrelations for temporal regions and spatial regions (notshown here).

u′ boundary of u =def ∀u′′. u′′ part of u′ (D4.8)⇒ u′′ straddles u

u =def u+ σu′(u′ boundary of u) (D4.9)u1 separate from u2 =def (D4.10)

¬(u1 overlaps u2) ∧ ¬(u1 overlaps u2)

A connected spatiotemporal region uc is not thesum of separate spatiotemporal regions. Nor is a con-nected temporal region tc the sum of separate tem-poral regions.

¬(∃u1, u2. uc = u1 + u2 (A4.1)

∧ u1 separate from u2)¬(∃t1, t2. tc = t1 + t2 (A4.2)∧ t1 separate from t2)

A scattered spatiotemporal region us(k) is the sumof k separate connected spatiotemporal regions. Like-wise a scattered temporal region ts(k) is the sum of kseparate connected temporal regions. We use the no-tation

∧k−1j=1 xj relxj+1 to mean x1 relx2∧x2 relx3∧

. . . ∧ xk−1 rel xk for relation rel.

∃uc1, . . . , u

ck. u

s(k) = uc1 + · · ·+ uc

k (A4.3)

∧k−1∧j=1

ucj separate from uc

j+1

∃tc1, . . . , tck. ts(k) = tc1 + · · ·+ tck (A4.4)

∧k−1∧j=1

tcj separate from tcj+1

We represent a scattered temporal region com-prised of k separate temporal intervals by vs(k).

5 Spatial, temporal and spatiotemporal pro-jections

The time projection function τ maps a process to its‘spell’, i.e. the temporal region corresponding to thetime during which the process endures. In BFO, wemake the assumption that there is no such thing asan instantaneous process, hence any process enduresthrough either a temporal interval v, or through ascattered temporal region vs(k) comprised of k tempo-ral intervals separated in time (A5.1). The spacetimeprojection function µ maps a process to its ‘span’,i.e. the spatiotemporal region corresponding to thearea of spacetime in which the process unfolds. Forany process there exists a spatiotemporal region inwhich that process unfolds (A5.2). The space projec-tion function ψ maps a process to its ‘spread’, i.e. thespatial region corresponding to the area of space overwhich the process covers. For any process there ex-ists a spatial region over which that process covers(A5.3). The time-indexed space projection functionψi maps an independent continuant at the temporalinstant i to the spatial region corresponding to thearea of space which the independent continuant oc-cupies at i. If an independent continuant exists at agiven temporal instant, then there is a unique spatialregion occupied by that continuant (A5.4 and A5.5).

∃v. (τ(p) = v) ∨ ∃vs(k). (τ(p) = vs(k)) (A5.1)∃u. µ(p) = u (A5.2)∃s. ψ(p) = s (A5.3)

a :Independent Continuant at i (A5.4)

⇒ ∃s. ψi(a) = s

ψi(a) = s1 ∧ ψi(a) = s2 ⇒ s1 = s2 (A5.5)

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If a process p1 is part of a process p2, then p1’s spellis part of p2’s spell. If a process p1 is part of a processp2, then p1’s span is part of p2’s span; moreover if p1’sspan is part of p2’s span then p1 is part of p2. If aprocess p1 is part of a process p2, then p1’s spread ispart of p2’s spread.

p1 part of p2 ⇒ τ(p1) part of τ(p2) (A5.6)p1 part of p2 ⇔ µ(p1) part of µ(p2) (A5.7)p1 part of p2 ⇒ ψ(p1) part of ψ(p2) (A5.8)

Note that BFO already features an expressiona located in s at i which is semantically equivalentto ψi(a) = s. Moreover in (Smith et al. 2005) anindependent continuant a1 is located in an inde-pendent continuant a2 at temporal instant i if andonly if there are spatial regions s1 and s2 such thata1 located in s1 at i and a2 located in s2 at i ands1 part of s2.

5.1 Temporal ordering

In BFO, all times are with respect to a single inertialframe of reference (making the ontology inadequatefor describing special relativity). The primitive bi-nary relational assertion i1 earlier than i2 is usedto order temporal instants along the time line. Al-though we do not show them here, we specify axiomswhich tell us that the temporal ordering relation isirreflexive, asymmetric and transitive.

Two non-equivalent temporal instants are seperateand one is earlier than the other.

i1 6= i2 ⇔ i1 separate from i2 (A5.9)⇔ (i1 earlier than i2 ∨ i2 earlier than i1)

According to the ontology, temporal instants onlyexist at the boundary of temporal intervals. Hencethe boundary of any temporal interval v is the sumof two temporal instants which are separated.

∃i1, i2. σt(t boundary of v) = i1 + i2 (A5.10)∧ i1 separate from i2

A temporal instant i1 starts a temporal intervalv if and only if i1 is the earlier instant lying at v’sboundary. Likewise, a temporal instant i2 ends atemporal interval v if and only if i is the later instantlying at v’s boundary.

i1 starts v =def (D5.1)∃i2. σt(t boundary of v) = i1 + i2

∧ i1 earlier than i2i2 ends v =def (D5.2)

∃i1. σt(t boundary of v) = i1 + i2∧ i1 earlier than i2

Every temporal interval is started and ended by atemporal instant.

∃i1, i2. i1 starts v ∧ i2 ends v (T5.1)∧ i1 earlier than i2

Proof. T5.1 follows from A5.10 with A5.9 and usingD5.1 and D5.2. �

5.2 Participation

The primitive ternary relational assertionp has participant a at i is used to specify thatindependent continuant a at temporal instant iparticipates in some way in process p. A processtype P has participant independent continuant typeA if and only if for all instances p of P there existssome a of A at some temporal instant i such thatp has participant a at i.

P has participant A =def ∀p. p :P (D5.3)⇒ ∃a, i. a :A at i

∧ p has participant a at i

For example: cell division has participantchromosome; photosynthesis has participantchlorophyll .

An independent continuant a exists at a tempo-ral instant i if and only if there is some process inwhich a is a participant at i. (An independent con-tinuant will at least participate in its own life.) Aprocess p occurs at at i if and only if there is someindependent continuant a which is a participant of pat i.

a exists at i =def (D5.4)∃p. p has participant a at i

p occurs at i =def (D5.6)∃a. p has participant a at i

If an independent continuant is instantiated at atemporal instant, then it exists at that temporal in-stant and vice versa. There are at least two temporalinstants at which any process occurs.

a :Independent Continuant at i (A5.11)⇔ a exists at i

∃i1, i2. p occurs at i1 ∧ p occurs at i2 (T5.2)∧ i1 6= i2

Proof. From A5.1 we know the spell of p is eithera temporal interval or a scattered temporal regionvs(k) comprised of k temporal intervals. If we choosethe former, T5.2 follows from A5.12 and T5.1. If wechoose the latter, T5.2 follows from A5.13, A4.4 andT5.1. We can use A4.4 since we know vs(k) is a tem-poral region by A2.12, A2.10, the transitivity of thesubtype relation, and T2.1. �

5.3 First and last instants

A temporal instant i is the first instant of a processp if and only if p occurs at i and does not occur at anytemporal instant before i. A temporal instant i is thelast instant of a process p if and only if p occurs ati and does not occur at any temporal instant after i.

i first instant of p =def p occurs at i (D5.7)∧ ∀i′. i′ earlier than i

⇒ ¬(p occurs at i′)i last instant of p =def p occurs at i (D5.8)

∧ ∀i′. i earlier than i′

⇒ ¬(p occurs at i′)

A process has unique first and last temporal in-stants.

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i1 first instant of p ∧ i2 first instant of p (T5.3)⇒ i1 = i2

i1 last instant of p ∧ i2 last instant of p (T5.4)⇒ i1 = i2

Proof. T5.3 can be proved by contradiction usingD5.7 and A5.9. T5.4 can be proved by contradictionusing D5.8 and A5.9. �

If the spell of a process p is the temporal intervalv and temporal instants i1 and i2 start and end v,respectively, then p occurs at both i1 and i2 and doesnot occur at any instant before i1 or after i2. If thespell of a process p is the scattered temporal regionvs(k) comprised of temporal intervals v1, . . . , vk andtemporal instant i1 starts v1 and temporal instant i2ends vk, then p occurs at both i1 and i2 and does notoccur at any instant before i1 or after i2.

τ(p) = v ∧ i1 starts v ∧ i2 ends v (A5.12)⇒ p occurs at i1 ∧ p occurs at i2

∧ ∀i′, i′′. (i′ earlier than i1∧ i2 earlier than i′′

⇒ ¬(p occurs at i′) ∧ ¬(p occurs at i′′))

τ(p) = vs(k) ∧ i1 starts v1 ∧ i2 ends vk (A5.13)⇒ p occurs at i1 ∧ p occurs at i2

∧ ∀i′, i′′. (i′ earlier than i1∧ i2 earlier than i′′

⇒ ¬(p occurs at i′) ∧ ¬(p occurs at i′′))

Any process has a first and last temporal instantsuch that the former is earlier than the latter. If thespell of a process p is the temporal interval v andtemporal instant i starts (ends) v, then i is the first(last) instant of p. If the spell of a process p is thescattered temporal region vs(k) comprised of tempo-ral intervals v1, . . . , vk and temporal instant i starts(ends) v1 (vk), then i is the first (last) instant of p.

∃i1, i2. i1 first instant of p (T5.6)∧i2 last instant of p ∧ i1 earlier than i2

τ(p) = v ∧ i starts v (T5.7)⇒ i first instant of p

τ(p) = vs(k) ∧ i starts v1 (T5.8)⇒ i first instant of p

τ(p) = v ∧ i ends v (T5.9)⇒ i last instant of p

τ(p) = vs(k) ∧ i ends vk (T5.10)⇒ i last instant of p

Proof. Using A5.1, if the spell of p is a temporal in-terval, then T5.6 can be proved by T5.1, A5.12, D5.7and D5.8. If the spell of p is a scattered temporal re-gion comprised of temporal intervals, then T5.6 canbe proved by T5.1, the transitivity of the temporal or-dering relation earlier than, A5.13, D5.7 and D5.8.T5.7 can be proved by A5.12 and D5.7, whereas T5.8can be proved by A5.13 and D5.7. T5.9 can be provedby A5.12 and D5.8, whereas T5.10 can be proved byA5.13 and D5.8. �

Using this theory we can define relations suchas preceded by and immediately preceded by,whereby a process p′ is preceded by a process p if

and only if the last temporal instant of p is earlierthan the first temporal instant of p′, and a processp′ is immediately preceded by a process p if andonly if there exists a temporal instant which is boththe first instant of p′ and the last instant of p.

6 Boundaries, fiat parts and aggregates of in-dependent continuants and processes

As shown in Figure 2, Boundary Of Object ,Fiat Part Of Object and Object Aggregate werefeatured in the original BFO (1.0 version) con-tinuant type hierarchy, along with Object andSite, as subclasses of Independent Continuant .All five types were considered mutually exclusive.Boundary Of Process, Fiat Part Of Process andProcess Aggregate, along with Process, were featuredin the BFO 1.0 occurrent type hierarchy as subclassesof Processual Entity . These four types were alsodeemed mutually exclusive. In the 1.0 version,Processual Entity has the same interpretation we(in this paper) have provided for Process, i.e. anentity which unfolds or develops in time, and whichdepends on one or more independent continuants.The type Process is interpreted as an entity that isa maximally connected spatiotemporal whole whichhas bona fide beginnings and endings. The candidateBFO (2.0 version) reflects the type hierarchy givenin Figure 1. The type Processual Entity has been re-named Process, and the old sense of Process (as beingan entity that is a maximally connected spatiotem-poral whole) has been removed, since these kinds ofprocesses occur rarely in reality. The type Objecthas been renamed Material Continuant . The typesBoundary Of Object , Fiat Part Of Object andObject Aggregate along with Boundary Of Process,Fiat Part Of Process and Process Aggregate havebeen entirely removed. This is because we mayonly talk of aggregations of material continuants, wecannot talk of, say, aggregations of fiat parts and/orboundaries. Moreover, it rules out entities whichare simultaneously fiat parts and aggregates, or say,boundaries and fiat parts.

Processual EntityProcessBoundary Of ProcessFiat Part Of ProcessProcess Aggregate

Independent ContinuantObjectSiteBoundary Of ObjectFiat Part Of ObjectObject Aggregate

Figure 2: Original BFO 1.0 Processual Entity andIndependent Continuant type hierarchy.

In this section we introduce a number of functionswhich still allow us to talk of boundaries, fiat partsand aggregates, as well as aggregations which includeboundaries and fiat parts.

6.1 Boundaries

The function βi maps a material continuant at thetemporal instant i to its boundary at i. We refer to

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its boundary as an ‘object boundary’. The functionβ maps a process to its boundary. Here we refer toits boundary as a ‘process boundary’. An object (orprocess) boundary can be thought of as that part ofa material continuant (or process) that exists exactlyat the limitation of that material continuant (or pro-cess). If a material continuant m exists at a temporalinstant i, then it has a boundary which is part of mat i. Furthermore, every process p has a boundarywhich is part of p.

m exists at i⇒ βi(m) part ofm at i (A6.1)β(p) part of p (A6.2)

The spatial region occupied by the object bound-ary of a material continuantm at the temporal instanti is the boundary of the spatial region occupied by mat i. The spread of a process boundary is the bound-ary of that process’ spread. Similar axioms hold forthe span and spell of a process and its boundary.

ψi(βi(m)) boundary of ψi(m) (A6.3)ψ(β(p)) boundary of ψ(p) (A6.4)µ(β(p)) boundary of µ(p) (A6.5)τ(β(p)) boundary of τ(p) (A6.6)

A material continuant type Mhas object boundary material continuant typeM ′ if and only if for all instances m of M at anytemporal instant i, βi(m) is an instance of M ′ at i.A process type P has process boundary process typeP ′ if and only if for all instances p of P , β(p) is aninstance of P ′.

M has object boundary M ′ =def (D6.1)

∀m, i. m :M at i⇒ βi(m) :M ′ at i

P has process boundary P ′ =def (D6.2)∀p. p :P ⇒ β(p) :P ′

The boundary of a cavity is the internal bound-ary of the material continuant which fully surroundsit. Other sites (such as hollows and tunnels) havea boundary which is the boundary of the containingwalls of the hollow or tunnel. For example a bound-ary of the interior of my coffee mug is the boundaryof the solid, containing part of the mug. The exter-nal, infinitely thin surface of an apple is a boundaryof the apple, but it is also a boundary of the sur-rounding air. A boundary of a tunnel bored into theapple is the boundary of the tunnel walls. Note thatthe boundary of the apple is part of the apple, butthe boundary of the surrounding air (tunnel) it is notpart of the surrounding air (tunnel).

6.2 Fiat parts

The function ϕi maps an independent continuant atthe temporal instant i to its fiat part. We refer toits fiat part as a ‘fiat object part’. The function ϕmaps a process to its fiat part. Here we refer to itsfiat part as a ‘fiat process part’. A fiat object (orprocess) part can be thought of as a part of an inde-pendent continuant (or process) which is demarcatedby human partitioning. In contrast, a bona fide ob-ject (or process) part of an independent continuant(or process) is demarcated by a discontinuity presentat physical gradients which is independent of humanpartitioning. We refer the reader to (Smith 2001) forfurther discussion regarding fiat parts. A fiat part of

an independent continuant a at the temporal instanti is a part of a at i. A fiat part of a process p is apart of p.

ϕi(a) part of a at i (A6.9)ϕ(p) part of p (A6.10)

An independent continuant type Ahas fiat object part independent continuant type A′if and only if for all instances a of A at any temporalinstant i, there exists a fiat part which is an instanceof A′ at i. A process type P has fiat process partprocess type P ′ if and only if for all instances p of P ,there exists a fiat part which is an instance of P ′.

A has fiat object part A′ =def (D6.3)

∀a, i. a :A at i⇒ ϕi(a) :A′ at i

P has fiat process part P ′ =def (D6.4)∀p. p :P ⇒ ϕ(p) :P ′

For example: lung has fiat object part upper lobe;body has fiat object part ventral surface.

If an independent continuant type A has a fiatobject part type A′ then A′ is a part of A. Likewiseif a process type P has a fiat process part P ′ then P ′is a part of P .

A has fiat object part A′ ⇒ A′ part of A (T6.1)P has fiat process part P ′ ⇒ P ′ part of P (T6.2)

Proof. T6.1 can be proved by D6.3, A6.9 and D3.2,since any independent continuant is a continuant byA2.15 and T2.1. Since any process is an occurrent byA2.3 and T2.1, T6.2 can be proved by D6.4, A6.10and D3.1. �

6.3 Aggregates

The function αi maps k independent continuantsa1, . . . , ak to their aggregation at the temporal instanti. We refer to their aggregation as an ‘object aggre-gate’. The function α maps k processes p1, . . . , pkto their aggregation. Here we refer to their aggrega-tion as a ‘process aggregate’. If k independent con-tinuants occupy separate spatial regions we can formtheir object aggregate. If k processes span separatespatiotemporal regions we can form their process ag-gregate.

k∧j=1

aj exists at i (A6.11)

∧k−1∧j=1

ψi(aj) separate from ψi(aj+1)

⇒ ∃a. αi(a1, . . . , ak) = a

k∧j=1

pj occurs at i (A6.12)

∧k−1∧j=1

µ(pj) separate from µ(pj+1)

⇒ ∃p. α(p1, . . . , pk) = p

If a is the object aggregate of independent contin-uants a1, . . . , ak at temporal instant i, then aj is partof a at i for 1 ≤ j ≤ k. If p is the process aggregate ofprocesses p1, . . . , pk, then pj is part of p for 1 ≤ j ≤ k.

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αi(a1, . . . , ak) = a (A6.13)

⇒k∧

j=1

aj part of a at i

α(p1, . . . , pk) = p⇒k∧

j=1

pj part of p (A6.14)

If a is the object aggregate of independent continu-ants a1, . . . , ak at temporal instant i, then the spatialregion occupied by a at i is the sum of the spatialregions occupied by each aj at i for 1 ≤ j ≤ k. If pis the process aggregate of processes p1, . . . , pk, thenthe spread of p is the sum of the spreads of each pjfor 1 ≤ j ≤ k. Similar axioms hold for the span andspell of a process aggregate.

αi(a1, . . . , ak) = a (A6.15)

⇒ ψi(a) =k∑

j=1

ψi(aj)

α(p1, . . . , pk) = p⇒ ψ(p) =k∑

j=1

ψ(pj) (A6.16)

α(p1, . . . , pk) = p⇒ µ(p) =k∑

j=1

µ(pj) (A6.17)

α(p1, . . . , pk) = p⇒ τ(p) =k∑

j=1

τ(pj) (A6.18)

An independent continuant type A is anobject aggregate of independent continuant typesA1, . . . , Ak if and only if for all instances a of A at anytemporal instant i, there exists instances a1, . . . , ak

such that αi(a1, . . . , ak) = a and aj is an instanceof Aj at i for 1 ≤ j ≤ k. A process type P is aprocess aggregate of process types P1, . . . , Pk if andonly if for all instances p of P , there exists instancesp1, . . . , pk such that α(p1, . . . , pk) = p and pj is aninstance of Pj for 1 ≤ j ≤ k.

A object aggregate of (A1, . . . , An) =def (D6.5)∀a, i. a :A at i

⇒ ∃a1, . . . , ak. αi(a1, . . . , ak) = a

∧k∧

j=1

aj :Aj at i

P process aggregate of (P1, . . . , Pn) =def (D6.6)∀p. p :P

⇒ ∃p1, . . . , pk. α(p1, . . . , pk) = p

∧k∧

j=1

pj :Pj

For example: string trio object aggregate of(violinist , violist , cellist); playing of a string trioprocess aggregate of (playing of violinist , playing ofviolist , playing of cellist).

If independent continuant type A is an object ag-gregate of independent continuant types A1, . . . , Akthen each Aj is a part of A for 1 ≤ j ≤ k. Likewise ifprocess type P is a process aggregate of process typesP1, . . . , Pk then each Pj is a part of P for 1 ≤ j ≤ k.

A object aggregate of (A1, . . . , An) (T6.3)

⇒k∧

j=1

Aj part of A

P process aggregate of (P1, . . . , Pn) (T6.4)

⇒k∧

j=1

Pj part of P

Proof. T6.3 can be proved by D6.5, A6.13 and D3.2,since any independent continuant is a continuant byA2.15 and T2.1. Since any process is an occurrent byA2.3 and T2.1, T6.4 can be proved by D6.6, A6.14and D3.1. �

6.4 DOLCE comparison

As a summary, it may be instructive for the reader tocompare the approach of BFO by contrast to that ofDOLCE. The Descriptive Ontology for Linguistic andCognitive Engineering has been developed at the Lab-oratory for Applied Ontology as a reference modulefor a library of ontologies which aims to provide ontol-ogy infrastructure for the Semantic Web. DOLCE hasa cognitive bias since it aims at capturing the ontolog-ical categories underlying natural language (Gangemiet al. 2002).

The hierarchy for DOLCE’s Endurant andPerdurant universals are shown in Figure 3. DOLCEtreats boundaries as instances of the universalFeature. Other features include holes, bumps, sur-faces and stains. Features are specifically dependenton physical objects which act as their hosts. DOLCEdoes not consider boundaries of perdurants, nor doesit consider fiat parts. Fiat parts are necessary for bi-ological representation, but have little relevance lin-guistically.

EndurantPhysical Endurant

Amount Of MatterFeaturePhysical Object

Non Physical EndurantArbitrary Sum

PerdurantEvent

AchievementAccomplishment

StativeStateProcess

Figure 3: DOLCE Endurant and Perdurant universalhierarchy.

In DOLCE, an amount of matter refers to massnouns, such as some air, some gold, some coffee. Aphysical object is an endurant with unity, and is al-lowed to change parts while keeping its identity. Ex-amples of non-physical endurants include poems, orideas. An arbitrary sum is a collection of endurantswhich has no overall unity and cannot be consideredan essential whole. Arbitrary sums change identity

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when they change parts. For example both my leftfoot and my car is an arbitrary sum. Thus DOLCEallows aggregations of boundaries and features alongwith other physical objects.

Perdurants (also called occurrences) in DOLCEare classified according to their cumulativity andhomeomericity. Hence the way aggregations of perdu-rants are formed in DOLCE is built into the universalhierarchy itself. Events are non-cumulative. For ex-ample the aggregation of two consecutive events offinishing a book does not form a new event whichis the finishing of a book. Events are differentiatedas achievements or accomplishments. Achievementsare instantaneous, for example: reaching the top ofa mountain, departing somewhere, or dying. Accom-plishments are non-instantaneous, for example: a per-formance, or climbing a mountain. Statives are cumu-lative and are differentiated as states and processes.States, such as sitting, or being red, are homeomeric.Each stage of a sitting occurrence is still a sitting oc-currence. Processes, such as running or writing arenon-homeomeric, since there are very short stages ofthese occurrences which do not involve running orwriting.

7 Conclusion

We have proposed the introduction of a numberof new functions in order to deal with boundaries,fiat parts and aggregates in Basic Formal Ontology.These functions are flexible enough to handle aggrega-tions of processes and independent continuants alongwith their fiat parts and boundaries, and we can alsouse these functions to express the fiat parts of bound-aries. We have introduced time, space and spacetimeprojection functions to improve upon the ontology’sexpressibility. We have formalised a simple temporaltheory using these functions.

References

Arp, R. & Smith, B. (2008), ‘Function, role and dis-position in Basic Formal Ontology’, in Proceedingsof the 11th Annual Bio-Ontologies Meeting.

Basic Formal Ontology website (2010), http://www.ifomis.org/bfo/home.

Casati, R. & Varzi, A. (1999), Parts and Places:The Structures of Spatial Representation, The MITPress.

DOLCE website (2010), http://www.loa-cnr.it/DOLCE.html.

Gangemi, A., Guarino, N., Masolo C., Oltramari A. &Schneider, L. (2002), ‘Sweetening Ontologies withDOLCE’, in Proceedings of the 13th InternationalConference on Knowledge Engineering and Knowl-edge Management LNCS 2473, 223–233.

Grenon, P. & Smith, B. (2004), ‘SNAP and SPAN:towards dynamic spatial ontology’, Spatial Cogni-tion and Computation: An Interdisciplinary Jour-nal 4(1), 69–104.

Relation Ontology website (2010), http://www.obofoundry.org/ro/.

Simons, P. (1987), Parts: A Study In Ontology, Ox-ford University Press.

Smith, B., Ceusters, W., Klagges B., Kohler, J., Ku-mar, A., Lomax, J., Mungall, C., Neuhaus, F., Rec-tor, A. & Rosse, C. (2005), ‘Relations in biomedicalontologies’, Genome Biology 6(R46).

Smith, B. (1996), ‘Mereotopology: a theory of partsand boundaries’, Data and Knowledge Engineering20, 287–303.

Smith, B. (2001), ‘Fiat objects’, Topoi 20(2), 131–148.

Spear, A.D. (2006), Ontology for the twenty firstcentury: an introduction with recommendations,http://www.ifomis.org/bfo/manual.

Zemach, E.M. (1970), ‘Four ontologies’, The Journalof Philosophy 67(8), 231–247.

80

Making Sense of Spreadsheet Data: A Case of Semantic WaterData Translation

Yanfeng Shu1 David Ratcliffe2 Geoffrey Squire2 Michael Compton2

1 Tasmanian ICT Centre, CSIROGPO Box 1538, Hobart, TAS 7001, Australia,

Email: yanfeng.shu@csiro.au

2 ICT Centre, CSIROGPO Box 664, Canberra, ACT 2601, Australia,

Email: {david.ratcliffe, geoffrey.squire, michael.compton}@csiro.au

Abstract

This paper intends to address the data ingestionproblem of the Bureau of Meteorology of Australia:data from over 240 water organisations have to betranslated into a standard water data transfer format(WDTF); meanwhile, the translated data have to beensured to comply with the Water Regulations 2008.Built on our previous work, in this paper, we followa knowledge-driven approach, i.e. using a knowledge-based information model to capture semantic gapsbetween data, WDTF, and the Regulations, and fur-ther to facilitate data translation and validation. Inparticular, we elaborate on the model design and itsmethodology. Further, we focus on the translation ofspreadsheet data, and introduce a mapping languagefor the expression of spreadsheet data, the model andthe mapping relationship between them. We haveimplemented a web application for spreadsheet datatranslation.

Keywords: Semantic data translation, informationmodel, mapping language.

1 Introduction

Recent years have seen high demand in Australia forimproving its efficiency of water management prac-tices (Ackland et al. 2005). In response to this, theBureau of Meteorology (BOM) has been given a man-date to build and maintain an integrated national wa-ter information system. Under the CommonwealthWater Act 2007, BOM is tasked with a range of func-tions which require it to collect, hold, manage, inter-pret and disseminate Australia’s water information.Section 126 of the Act provides for the establishmentof Regulations to support these functions, which cameinto effect on 30th June 2008. The Water Regula-tions 2008 1 define the requirements for the collection

This work is part of the water information research and devel-opment alliance between CSIRO’s Water for a Healthy CountryFlagship and the Bureau of Meteorology. The work is sup-ported by the Tasmanian ICT Centre. The Tasmanian ICTCentre is jointly funded by the Australian Government throughthe Intelligent Island Program and CSIRO. The Intelligent Is-land Program is administered by the Tasmanian Departmentof Economic Development, Tourism and the Arts. The authorswould like to thank Gavin Walker for the comments on thepaper draft.Copyright c©2010, Commonwealth of Australia. This paperappeared at the Sixth Australasian Ontology Workshop AOW2010), Adelaide, Australia. Conferences in Research and Prac-tice in Information Technology (CRPIT), Vol. 122, ThomasMeyer and Mehmet A. Orgun and Kerry Taylor, Ed. Repro-duction for academic, not-for profit purposes permitted pro-vided this text is included.

1http://www.bom.gov.au/water/regulations/.

Category Information1 Watercourses2 Ground water resource3 Major and minor water storages4 Meteorological information5 Water use6 Water rights, allocations and trades7 Urban water management8 Water restrictions9 Water quality10 Descriptive and reference information

Table 1: Water information categories as specified inthe Regulations.

of water data by BOM in 10 categories (as shown inTable 1), with each category further defined by sub-categories.

The Regulations also specify the organisations whomust provide specified water information to the Bu-reau and the time in which they must provide it. Over240 organisations are involved. These organisations,as revealed by an online survey conducted by the Bu-reau in 2008, use a wide range of systems and dataformats. An examination of data from organisationsshows that various structural and semantic hetero-geneities are present.

To ensure robust and reliable data delivery,the Bureau and Australia’s Commonwealth Scien-tific and Industrial Research Organisation (CSIRO)have developed a Water Data Transfer Format(WDTF)2 (G.Walker et al. 2009), and established itas the standard for data transfer 3. The first ver-sion of WDTF was produced in August 2008, withthe current version 1.0 released in September 2009.WDTF is an XML format built on the InternationalStandard Organisation’s General Feature Model, ISO19109, and the Open Geospatial Consortium (OGC)’sObservations and Measurements (O&M) model (Cox2007a,b). It has been designed, in general, in accor-dance with the Regulations requirements. Neverthe-less, its interpretation of the requirements may notfully capture the semantics as implied by the Regula-tions.

As a result, data in various representations have tobe translated into WDTF; also, the translated datahave to be validated to ensure that they comply withthe Regulations. The current practice of the Bureaumainly focuses on WDTF data validation, while leav-ing the task of data translation largely to each or-ganisation. The translation work proves to be non-

2http://www.bom.gov.au/water/regulations/wdtf/.3BOM Water Information Bulletin, Issue 5, 16 February 2009,

http://www.bom.gov.au/water/publications.

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Figure 1: Semantic data translation process.

trivial, especially for those small organisations whichtypically do not have the capability for doing this. Toperform the translation, one needs to be familiar withWDTF, its structure, elements and related semantics,in order to know what data needs to be translated andhow. Besides that, it is time-consuming and error-prone if the translation is done manually, consideringthe number of data sources and the volume of datainvolved.

To address this, in our previous work (Shu et al.2010), we proposed a knowledge-driven approach, inwhich knowledge models are used to capture semanticgaps between data, WDTF, and the Regulations, andfurther to facilitate data translation and validation.Based on the approach, data translation is done asshown in Figure 1. Given data from an organisation,it is first mapped onto the models and enriched withthe semantics provided by them. Then a mappingbetween data and WDTF is generated which spec-ifies how data is translated into WDTF. Based onthe mapping, a query is generated for data transfor-mation. Finally, when the query is executed, datais transformed into a corresponding WDTF instancedocument.

In the previous work, we only sketched the modeldesign and discussed briefly the design methodol-ogy. In this paper, we elaborate on the design of themodel, including how the model is designed to facili-tate mapping between data and the model, mappingbetween the model and WDTF, and compliance withWDTF/Regulation constraints. We also describe indetail main concepts, relationships and constraintscovered by the model.

Further, in this paper, we focus on the transla-tion of spreadsheet data (in our previous work, weassumed that data have already been in a struc-tured format before translation, e.g. relational ta-bles). Spreadsheets are commonly used by organisa-tions to store their data. Characteristics of spread-sheet data include implicit and irregular structure,unfixed schema, nested data (Kovatchev 2007). Allthese characteristics pose challenges for mapping datato the model. One is the expression of spreadsheetdata. For this, we introduce a mapping languagewhich provides a way to express not only the partof spreadsheet data to be mapped, but also the partof the model to be mapped to, and the associationbetween them.

We have implemented a web application whichprovides a GUI frontend for users to map spreadsheetdata to the model. The generation of WDTF instancedocuments is supported by a back-end with the pro-cessing of instance data in the model.

The rest of the paper is organised as follows. Sec-tion 2 describes the information model in detail; Sec-tion 3 introduces the mapping language for associat-ing spreadsheet data to the model; Section 4 givesthe implementation details of the web application wehave developed for spreadsheet data translation; fi-nally, Section 5 concludes the paper and points outfuture work.

2 Information Model

In this section, we first review the information sourcesinvolved in the model design. Then we discuss thedesign methodology, and finally describe major con-cepts, relationships and constraints considered in thedesign.

2.1 Information Sources

Three major information sources are involved in theBureau’s data ingestion: the Regulations, WDTF,and data from organisations.

2.1.1 The Regulations

The Regulations specify, among others, the water in-formation to be supplied to the Bureau. Table 2shows part of water storage information (Category 3of Table 1). Each subcategory in the Regulations typ-ically corresponds to an observation of a propertyof a feature. For example, 3a in Table 2 is about anobservation of water level of a major storage.

Along with an observation, some context informa-tion is typically required, e.g. what is measured? inwhich unit? any feature of interest? etc. These in-formation requirements, in general, can be inferred ascertain constraints on an observation. In the case of3a, for example, it is required that the water level ofa storage be measured in metres; also, when the mea-surement is taken, the time of the observation, andthe datum used, be recorded.

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Subcategories Water storage information (Category 3)3a Level of water held in a major storage, expressed in me-

tres relative to specified datum, and the time of the ob-servation

3b Volume of water held in a major storage, expressed inmegalitres, and the time of the observation

3c Total daily volume of water released from a major stor-age to a watercourse, expressed in megalitres per day,the start and finish times of the observation, and date ofthe observation

... ...

Table 2: Information on major and minor water storages as specified in the Regulations.

Figure 2: A snippet of a WDTF instance document.

2.1.2 WDTF

WDTF, on the other hand, does not specify the in-formation required for a particular observation type(like 3a in Table 2). Rather, it classifies observationsinto the following four general types based on bothOGC O&M specifications and common practices inthe water domain:

• WaterQualityObservation: observations ofspecimens regarding water quality;

• ComplexObservation: observations of gaug-ings for conversions between multiple propertiesat the same time.

• TimeSeriesObservation: observations of sin-gle properties over time;

• GeometryObservation: observations of geom-etry surveys.

For each of these observation types, WDTF definesthe information to be provided. Figure 2 shows partof a WDTF instance document (for TimeSeriesOb-servation). As shown, WDTF also asks for informa-tion such as the property and feature of interest (i.e.observedProperty and featureOfInterest respec-tively). Often, it asks more than what the Regula-tions do. However, due to the general nature of thedefinitions of observations, the relationships between

a particular observation type, the feature of interest,the property observed and the unit used, cannot bespecified and are thus loosely constrained.

2.1.3 Data from Organisations

Data from organisations are provided by basicallyfollowing the information classification of the Reg-ulations. However, they typically do not includeenough context information required for data trans-lation. Examples of such information include that re-quired for appropriate data interpretation, e.g. whichfeature or observation the data is related to? Figure 3gives a few examples of spreadsheet data from organ-isations 4. All these examples are very simple, butthey include little information about what the data isabout. Without such information, it is very difficultto do the translation, as the data can be interpretedin different ways.

These examples also indicate that various termi-nologies may be used to describe data. This includesthe possibility that different names may be used to de-note the same thing, or the same names may be usedto denote different things. For example, contents in(b) is the same as volume in (c); on the other hand,volume in (a) is different from volume in (c) due to

4Data used in this paper are changed with values modified andidentifying information removed.

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Figure 3: Spreadsheet data examples.

different contexts (while the former denotes the vol-ume of water usage, the latter the volume of waterheld in the storage). Further, various value represen-tations may be used for the same property, or variousmeasurements may be taken for the same observation.For example, levels of a storage can be measured inmetres, or feet; or a storage can be observed by itslevel and volume, or by the percentage of water heldin the storage as is the case in (d).

2.2 Design Methodology

The main use of the information model is to act as anintermediate schema between data and WDTF, whichis, on the one hand, easy for users to understand andmap their data to, and on the other hand, easy forthe system to map to WDTF. As such, users need notknow the details of WDTF as its essential informa-tion has already been captured by the model. Also,the model is used as a kind of data validator, whichhelps verify whether data provide all necessary infor-mation, and ensure that data, once translated, satisfyall constraints imposed by WDTF and the Regula-tions. Therefore, the model should be designed tofacilitate the followings:

Mapping between data and the modelMapping between data and the model isessentially the process of enriching data withthe semantics provided by the model. To makethis process easier, it is desirable for the modelto have a similar information classification asthe one used by the Regulations. As mentionedearlier, data being provided basically followthe same classification. Thus, by having asimilar classification in the model, users canquickly identify relevant parts of the modelwhich correspond to data semantics. Also, tofacilitate automatic mapping, it is desirablefor the model to capture various terminologies(e.g. synonyms and abbreviations), and to covercommon modelling alternatives (e.g. differentunits used for the same property).

Mapping between the model and WDTF Thislargely depends on how the model covers theinformation of WDTF. If every piece of WDTFis covered, then the mapping is certainly easy.However, this is not necessarily the case asWDTF includes a lot of XML schema-specificdetails which are not relevant to data. Also,

this makes the model not easy for users to un-derstand. To avoid this and also to ensure easymapping, the model should include the followinginformation of WDTF: (1) data-related, whichcan be provided by users, e.g. the name of afeature; (2) domain-related, which is commonlyused in domain practices and can be easily un-derstood by users, e.g. a time-series observationwhich consists of a set of observations but withits own specific properties.

Compliance with WDTF/Regulations constraintsThe model should only cover the constraintswhich are relevant to the water domain. Thereare two kinds of such constraints in WDTF:(1) strict constraints, as represented by XMLrestrictions, e.g. a feature must have a name;(2) loose constraints, as imposed by XMLforeign referential relationships, e.g. the onewe illustrated earlier about the relationshipsbetween observations, features, properties andunits. Both these kinds of constraints need tobe captured in the model; loose constraints canbe further refined by the constraints implied inthe Regulations.

2.3 Major Concepts, Relationships and Con-straints

With the above methodology in mind, we developedthe information model in OWL2 5 with Protege 4.1 6.We choose OWL mainly because of its expressivityand reasoning support. OWL is expressive enough torepresent the concepts, relationships, and constraintswhich we need to cover in the model (with the supportof SWRL rules 7). Also, its reasoning support allowsus to perform data validation automatically.

The model we developed is different from existingefforts (Henson et al. 2009, Probst 2006) which focuson creating an ontological representation of O&M,though they share some common concepts. A keyconcept of our model is Observation. Following thedefinition of (Cox 2007a), “an observation is an act ofobserving a property or phenomenon, with the goal ofproducing an estimate of the value of the property.”Associated with Observation, there are concepts suchas Feature, Property, Location, and Time. For eachobservation, there are exactly one observed property,

5http://www.w3.org/TR/owl2-profiles/.6http://protege.stanford.edu/.7http://www.w3.org/Submission/SWRL/.

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Figure 4: The observation class hierarchy.

Figure 5: SWRL rules for the representation of constraints.

one estimated value of the property, one procedureused to generate the value, and one observation lo-cation and time. We represent this in OWL2 withqualified cardinality restrictions:

Observation v (=1hasProperty .Property) u(=1hasValue.xsd :anyType) u(=1hasProcedure.xsd :string) u(=1hasLocation.Location) u(=1hasTime.Time)

Observations are classified according to the waterinformation category of the Regulations. Figure 4shows part of the observation class hierarchy. Eachsubclass may introduce new restrictions or refine in-herited ones. For example, WaterCourseLevelObser-vation introduces two new restrictions and inheritsone from WaterCourseObservation:

WaterCourseLevelObservation vWaterCourseObservation u(=1hasLevelDatum.xsd :string) u(=1hasWaterLevel .Length) u(=1hasFeature.WaterCourse) u...

Each property is defined to be measured in one typeof unit. For example,

Length vProperty u(=1hasUnit .LengthUnit)

There is no restriction on which length unit is used,and data can be mapped onto the model, as long asthe unit used is a subclass of LengthUnit. This largelyfacilitates the translation of data in different valuerepresentations.

A set of observations constitute ObservationCol-lection, defined as

ObservationCollection ≡∀hasMember .Observation u∃hasMember .Observation

We model each observation type in WDTF as a sub-class of ObservationCollection 8, e.g. TimeSeriesOb-servation. Each has its own specific properties. Forexample, a time-series observation consists of obser-vations which share the same observed property, thesame procedure, the same location but have differentobservation times. We define this with SWRL rulesas shown in Figure 5.

3 Mapping between Spreadsheet Data andthe Information Model

To map spreadsheet data to the information model,we use a simple mapping language. A mapping inour language is a statement expressing how sourcedata from a spreadsheet form part of the ABox of themodel.

8Note WaterQualityObservation is modelled in WDTF asan observation on a specimen. Here we introduce WaterQuali-tyObservations as a set of observations which measure multipleproperties of the same specimen.

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3.1 Source to Target Mapping

For simplicity of presentation, in this paper, we ex-press a mapping informally. A mapping generallystates that for each variable x in x satisfying sourceconstraints, there exists y in y satisfying target con-straints, such that the value of y depends on x. Inour case, a mapping consists of two components: asource component expressing which part of spread-sheet data to be mapped and relationships among thedata, and a target component expressing which partof the model to be mapped to.

3.1.1 Source Component: Spreadsheet Data

Data from a spreadsheet (also called a workbook,which may contain several sheets) can be identifiedby sheet number and cell range, denoted as S.Xm:Y z,where S is a sheet number, X (Y ) is a column iden-tifier, m (n) is a row number, and Xm:Y z is a rangeof cells starting at location Xm and ending at Y n.

Cells within a range can be ordered by indi-cating whether they are in row-major or column-major order. For example, 0.B2:A1RowMajor (i.e.in row-major order) represents the ordered listof cells [B2, A2, B1, A1], and 0.A1:B2ColMajor (i.e.in column-major order) represents [A1, B1, A2, B2],where all cells are from sheet 0. By default, column-major order is assumed.

Cells can also be partitioned by row or column us-ing p row or p col. For example, p row 0.A2:B1(where the cell range has either row or column-major order) represents a partitioning by row, i.e.[[A2, B2], [A1, B1]].

Furthermore, several functions are used to operateon lists and express relationships between cells (e.g.by grouping cells into tuple structures):

• product R S 9: used for associating each ele-ment in list R with each element in list S. For ex-ample, product 0.X5:X5 0.A1:A2 denotes thatcell X5 in sheet 0 is associated to all cells in0.A1:A2, which represents the ordered list of tu-ples [(X5, A1), (X5, A2)].

• zip R S 10: used for associating each ele-ment in list R with each element in list S inone-to-one order preserving correspondence be-tween elements of R and S. For example,zip [(X5, A1), (X5, A2)] 0.E5:E6 denotes thattuple (X5, A1) and (X5, A2) are associated withE5 and E6 respectively, which represents the or-dered list of tuples [(X5, A1, E5), (X5, A2, E6)].

• map f R 11: used for applying functionf to each element in R. For example,map (product 0.X5:X5) [[A2, B2], [A1, B1]]represents [[(X5, A2), (X5, B2)],[(X5, A1), (X5, B1)]].

Data which are not included in a spreadsheetbut directly provided by users during mapping,e.g. constant data, are represented in collectionssuch as ordered lists, for example, a list of dates[1/1/2010, 1/2/2010, ...].

3.1.2 Target Component: the Model

We use a tree-like expression (similar to a Descrip-tion Logic concept expression) to express the part

9product R S is an operation equivalent to a list comprehensionof the form [(r, s) | r ← R, s ← S].

10zip R S is an operation equivalent to a list comprehension ofthe form [(r, s) | r ← R | s ← S].

11map f S is a partial function application, i.e. [f s | s ← S].

of the model to be mapped to. It has a form of(C1 u (p1.C2, ...), (p2 u (C3 u p4, ...))) where Ci is aclass name (C1 is the name of a top class), and pj isan object or datatype property name. Such an expres-sion is expected to conform to the model semantics,i.e. it must not be unsatisfiable with respect to theTBox of the model.

3.1.3 A Mapping Example

By combining source (spreadsheet and constant data)and target (model) expressions, we can associatesource data with instances of the model. For example,consider the following source spreadsheet data:

A B C1 Dam 1 Dam 22 May 55 773 June 57 784 July 61 78

Also assume the following OWL axioms of the targetontology (a simplified version of the model in Sec-tion 2) in describing the data in this spreadsheet:

TimeSeriesObservation v=1hasLocation.xsd :string u≥1hasMember .Observation

Observation v=1hasTime.Date u=1hasValue.xsd :anyType u=1hasProperty .Property

Property v=1hasUnit .UnitOfMeasure

Then a mapping which expresses the relationship be-tween the data and the ontology will be as follows:

TimeSeriesObservation uhasLocation.(l) uhasMember .(Observation u

hasTime.(d) uhasValue.(v) uhasProperty .(Volume u

hasUnit .(ML)))

Where l, d, v satisfy:

l ∈ L where L = 0.B1:C1

d ∈ D where D = 0.A2:A4

v ∈ V where V = 0.B2:C4

map (zip D) (p row V )

map (zip L) (p col V )

map (product [ML]) V

The first of the map expressions above relates val-ues for month (D) with values of dam volume (V ) overrows; the second relates each dam identifier (L) withthe same values (V ), but over columns; and the thirdrelates each value of dam volume (V ) to an ontologyinstance ML which represents the unit of measure ofmegalitres.

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3.2 Mapping Evaluation

When a mapping is evaluated over a source spread-sheet and a target ontology, we seek to generate in-stances which satisfy both source constraints (i.e. as-sertions through source expressions) and target con-straints (i.e. the ontology TBox).

Continuing the previous example, we now il-lustrate how a mapping is evaluated. We evalu-ate a mapping in a bottom-up manner, by firstgenerating data for concepts and properties atthe leaves of the expression. In the example,source data have been mapped to the leaves ofthe target expression with variables l (locations), d(month data), v (volume measurement data), andthe ontology instance ML. Firstly, property asser-tions for hasLocation may be generated, evaluat-ing to the set {(t1, “Dam1”){B1}, (t2, “Dam2”){B2}},where t1, t2 are variables representing instances ofTimeSeriesObservation. Each element in the set islabelled with a set of source references from whichit is generated. Note that the values for t1, t2 willnot be generated unless all constraints specified onhasLocation against TimeSeriesObservation are in-spected. Since a functional relationship is present (i.e.the = 1 cardinality restriction), it is implied that t1and t2 are unique, as “Dam 1” and “Dam 2” are dif-ferent. Similarly, assertions for the hasUnit propertyevaluate to the set {(p1,ML)}, where p1 is an instanceof class Property .

Assertions for hasProperty evaluate to{(o1, p1){ML}}, hasTime to {(o2, “May”){A2},(o3, “June”){A3}, (o4, “July”){A4}}, and hasValue to{(o5, 55){B2}, (o6, 77){C2}, (o7, 57){B3}, (o8, 78){C3},(o9, 61){B4}, (o10, 78){C4}}. Each oi generated hereindicates an instance of class Observation, but notall of them imply unique instances. In fact, we seekto group property values for particular instancesof Observation, by conforming to cardinality con-straints on the properties against the class, andalso the assertions made on the source data. Forexample, each Observation is related to exactly onehasValue assertion, of which there are six, whichimplies that o5 to o10 are distinct. Also becausewe assert map (product[ML]) V which meansthat the instance ML is to be related with each ofhasValue assertions, and each Observation instanceis related to exactly one Property instance viahasProperty as generated from the instance ML, weneed to distribute the assertion {(o1, p1){ML}} acrossall hasValue assertions {(o5, 55){B2}, (o6, 77){C2},(o7, 57){B3}, (o8, 78){C3}, (o9, 61){B4}, (o10, 78){C4}}.

Similarly, we are required to relate o2, o3 and o4(as generated from set D, the month values) to eachof the distinct instances o5 to o10 (as generated fromset V , the dam volume values). For this, we referto the assertion map (zip D) (p row V ), which re-lates each of the items in D to V grouped into col-lections by row, i.e. associating (o2, “May”){A2} toeach hasValue assertion generated from row 2, namely{(o5, 55){B2}, (o6, 77){C2}}, and so on for rows 3 and4.

After processing the instance assertions for everyproperty of Observation in the mapping expression,we obtain the set for property hasValue,

{(o5, 55){B2}, (o6, 77){C2}, (o7, 57){B3},(o8, 78){C3}, (o9, 61){B4}, (o10, 78){C4}};

the set for property hasProperty ,

{(o5, p1){ML}, (o6, p1){ML}, (o7, p1){ML},(o8, p1){ML}, (o9, p1){ML}, (o10, p1){ML}};

and the set for property hasTime,

{(o5, “May”){A2}, (o6, “May”){A2},(o7, “June”){A3}, (o8, “June”){A3},(o9, “July”){A4}, (o10, “July”){A4}}.

Note that all oi are also asserted to be instances ofclass Observation.

The last part of the evaluation is to evalu-ate the instances of the TimeSeriesObservationclass, which is restricted by the hasLocation andhasMember properties. As mentioned earlier, theset of assertions evaluated for hasLocation are{(t1, “Dam1”){B1}, (t2, “Dam2”){C1}}, and t1, t2are unique because of the functional restriction onhasLocation. However, the property hasMember doesnot have a functional restriction; and the multipleassertions evaluated for this property (namely,

{(t3, o5){B2,A2,ML}, (t4, o6){C2,A2,ML},(t5, o7){B3,A3,ML}, (t6, o8){C3,A3,ML},(t7, o9){B4,A4,ML}, (t8, o10){C4,A4,ML}})

do not imply unique instances ofTimeSeriesObservation, specifically, t3 to t8 arenot constrained to be unique. Therefore, in orderto group these instances into unique t1 and t2, werefer to the last of the source grouping assertions,map (zip L) (p col V ), which relates each damlocation in L to dam volume measurement values Vgrouped into collections by column, thus unifyinginstance t1 to t3, t5 and t7, and t2 to t4, t6 and t8.

Thus the final evaluation results in the followingset of instance assertions

{(t1, o5){B2,A2,ML}, (t2, o6){C2,A2,ML},(t1, o7){B3,A3,ML}, (t2, o8){C3,A3,ML},(t1, o9){B4,A4,ML}, (t2, o10){C4,A4,ML}}

for property hasMember , along with the set{(t1, “Dam1”){B1}, (t2, “Dam2”){C1}} for propertyhasLocation. Note that all ti are also asserted to beinstances of TimeSeriesObservation.

Each of the instance assertions of classes or prop-erties, once finalized, can be asserted into the ABoxof the ontology.

4 Implementation

We have implemented a web application providinga GUI frontend for users to load spreadsheets into,view an OWL ontology encoding the informationmodel, and compose mapping expressions betweenthem. Figure 6 shows the user interface.

Our implementation of the mapping language isbased on JSON 12. We have implemented a mappingparser or interpreter which translates mappings ex-pressed in JSON into the one described in Section 3,with source expressions over spreadsheet data andtarget expressions over the model.

The evaluation of mappings is done by a map-ping evaluator, and Apache POI is used to interro-gate spreadsheet data in Microsoft Excel format. Theevaluator also interfaces with the OWL ontology us-ing Jena 13 and incorporates the use of Pellet 14, anOWL2 reasoner. It may be worth mentioning that weuse Pellet to perform incremental consistency check-ing when evaluating a mapping and asserting new in-stances into the ABox of the model. This allows usto perform fast run-time consistency checking.

The mapping implementation is complementedwith a back-end to retrieve instance data from themodel using SPARQL 15. Once retrieved, data ren-

12http://www.json.org/.13http://jena.sourceforge.net/.14http://clarkparsia.com/pellet/.15http://www.w3.org/TR/rdf-sparql-query/.

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Figure 6: A web application for spreadsheet data translation.

dered in XML are processed with XQuery scripts togenerate WDTF XML instance documents. We arecurrently working on extending the back-end to incor-porate the transformations that serve to manipulateintermediate data prior to the generation of WDTFdocuments, for example, unit conversion or data ag-gregation.

5 Conclusion and Future Work

In this paper, we addressed the Bureau’s data inges-tion problem by following the same knowledge-drivenapproach which we proposed in previous work, i.e.using a knowledge-based information model to cap-ture semantic gaps between data from organisations,WDTF, and the Regulations, and further to facili-tate data translation and validation. In particular,we described in detail the model design which wasonly sketched in the previous work, including its in-formation sources and design methodology. Further,we targeted a particular and common data format,namely spreadsheets, and introduced a mapping lan-guage for the expression of spreadsheet data and themappings between data and the model. Finally, wedescribed the web application we have implementedthat provides a GUI frontend for users to map spread-sheet data to the model.

Though the model we developed is designed fora specific problem in the water domain, the way inwhich the model is used can be applied to similardata integration problems in other domains. Also, theway in which we characterise and express spreadsheetdata is useful for those applications (e.g. ETL tools)which need to extract data from spreadsheets. Ourcurrent mapping language is still too data-oriented inthat source expressions can only be defined in termsof absolute positions in the spreadsheet. Thus map-pings cannot be reused for other spreadsheets unlessthey have the same kinds of data in the same struc-tures in the same locations. In the future, we intendto extend our mapping language and make it moreabstract and structure-oriented so that mappings canbe reused. Also, the current model mainly consid-ers water information categories about observations.This needs to be extended to cover other categoriessuch as water rights and restrictions.

References

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