GeoInfo 2005 GIScience and Relationships Werner Kuhn Muenster Semantic Interoperability Lab (MUSIL)

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GeoInfo 2005

GIScience and Relationships

Werner KuhnMuenster Semantic Interoperability Lab (MUSIL)

GeoInfo 2005 Relationships

Who arrived here by bus?

How do you know? What is a bus? WordNet:

• a bus is a „vehicle carrying many passengers; used for public transport”

type of public transport• a public transport is a „conveyance for passengers or mail or

freight”type of conveyance

• a conveyance is „something that serves as a means of transportation”

type of instrumentation

etc. ... So, what makes a bus a bus?

• The hierarchy of public transport – conveyance – instrumentation?


Context

Such questions arise in information retrieval„show me all bus connections to Campos do Jordao“

... and in information integration„show me a map of public transportation in Brasil“

They are, of course, semantic questions.



My thesis today

1. Relationships are the core of semantics

2. GIScience (and other information sciences) lack an understanding of basic relationships

3. Semantic tools limit what we can say about relationships

4. A better understanding will produce better information science and better tools


Overview

1. A brief History of Relationships in GIScience

2. Two Case Studies: Boathouse, Ferry

3. Toward Foundational Relationships

4. Formalization and Implementation

5. Conclusions


Brief History of Relationships in GIScience

A relationship (or relation) is

an association between two or more individuals or universals

1888 Peano Set membership

1950 Moran Spatial autocorrelation

1965 Zadeh Fuzzy set membership

1975 Freeman Spatial relations

1977 Tversky Similarity

1977 Gibson Affordances

1983 Allen Temporal intervals

1986 Herskovits Spatial prepositions

1987 Simons Mereological relations

1990 Kuhn Geometric relations

1991 Egenhofer Point-set topological relations

1991 Barrera Temporal relations

1992 Frank Qualitative distances and directions

1992 Freksa Qualitative directions

1992 Randell Region-connection relations

2004 Smith Foundational relations

2005 Bittner Spatial relations between classes

Relations between what ?

individual set type

individual temporal

spatial

mereological

affordance

conceptual

lexical

membership instance-of

set inclusion model

type is-a

similarity

statistics

others ???


Are Types just Sets of Individuals?

If true, all relations on types can be defined in terms of relations on individuals

True for is-a relation• A is-a B, iff for all a:A a:B• cats are animals, iff every cat is an animal

Not true for similarity!• ?A is similar to B, iff every a:A is similar to every b:B• ?cats are similar to dogs, iff every cat is similar to every dog• similarity relations are not defined in terms of individuals


=> Types are not Sets

The notion of class in ontology unfortunately blurrs this distinction

The notion of type in computing is more restricted than the one used here• a value or object can (usually) only have one type

An alternative term for type is universal


Case Study 1

What is the relation between a boat and a house in a „houseboat“?

What is it in a „boathouse“? What kind of relations are these?

Structure

Boathouse

House

Artifact

is a

is a

is a

Houseboat

Boat

is a

Conveyance

is a

is a

A concept DAG (simplified from WordNet)

storing

Waterbody

at edge of

Housing

supporting

is a

People

housing

onconveying


What kind of relations ?

1. between types2. not only is-a3. no multiple is-a4. some part-of (omitted, implicit in „structure“)5. spatial (defining meaning of types!)6. also: agent, causation, ... 7. note: not just binary relations


Conclusion from Case Study 1

A limitation to is-a relations strips out essential semantics• cf. glosses in WordNet

Today‘s semantic web imposes this limitation• subsumption reasoning only

Needed: a way to model richer relations • without resorting to multiple is-a (OntoClean)• retaining decidability and reasoning efficiency


Case Study 2

How do road elements and a ferry lines relate to a transportation network ?

TransportationLink

Road Element Ferry Line

Way

Road

Artifact

is a

is a

A concept DAG (simplified and extended from WordNet)

Mediumon

Ferry Line

is a

FerryCar

moving-on Conveyance

is a

is a is a

supporting

WaterLand

is a is a


Conclusion from Case Study 2

Supports all conclusions from case study 1• our ontologies are „relationship-poor“

Significant overlap of types and relations between the two case studies

But: this is getting too complex !• need to apply Ockham‘s razor• can we classify the relations ?


Toward Foundational Relations for GIScience

The list from the case studieson, supporting, moving-on, conveying,housing, storing, at-edge-of

All additional relations between types in the two case studies are spatial !


Structure

Boathouse

House

Artifact

is a

is a

is a

Houseboat

Boat

is a

Conveyance

is a

is a

A concept DAG (simplified from WordNet)

storing

Waterbody

at edge of

Housing

supporting

is a

People

housing

onconveying


Way

Road

Artifact

is a

is a

A concept DAG (simplified and extended from WordNet)

Mediumon

Ferry Line

is a

FerryCar

moving-on Conveyance

is a

is a is a

supporting

WaterLand

is a is a


A proposal for foundational relations

1. Containment: housing, storing

2. Support: on

3. Path: moving-on

4. Contact: at-edge-of

5. ...


What are these relations ?

All are image schematic• based on sensory-motor patterns of experience• proposed as basic cognitive structures [Talmy, Langacker, Lakoff, Johnson, ...]

• invariant in semantic mappings• combinable!


Containment Schema

relates two types: container, item

isIn?

operations: enter, isIn, exit


Support Schema

relates two types: surface, item

isOn?

operations: putOn, isOn, takeOff


Path Schema

relates three types: locations, path, item

operation: move

Combining Support and Path


Formalizing Relationships

Between individuals: predicatesbefore (Tuesday, Wednesday) contains (Brasil, Campos do Jordao)

Between sets: set theory (predicates)(all GeoInfo2005 slides) (this slide set)

Between types: ???a bus is a conveyance for passengersa boathouse is a house for boats


Proposed Formalization

types modeled as theories [Goguen]• not as predicates • with operations and (equational) axioms• a boathouse theory with operations to store/retrieve boats

theories are parametrized • a house theory has a parameter for what is stored

relations between types are theory morphisms• unification of parameters with other types• the boathouse type unifies the „stored“ parameter in the house

theory with the boat type


Boathouse Example (simplified)

class HOUSE house entity

class BOAT boat

class (HOUSE boathouse boat, BOAT boat) => BOATHOUSE boathouse boat

HOUSE gets enter/exit operations from CONTAINMENT BOAT gets move operation from PATH, on water from SUPPORT


Implementation

in Haskell (Hugs)• using type classes• tested with arbitrary data types and instances as models

set of equational theories for (case of boathouse)• 9 schemas: containment, support, link, path, contact, collection, cover, part-whole, location

• 28 types: conveyance, vehicle, boat, house, boathouse, houseboat, ...


Results

A formal account of essential aspects of geospatial semantics

second order (parametrized) equational theories and morphisms

Tested with boathouse and ferry use case

Kernel of a semantic reference system• referencing by instantiation

instance BOATHOUSE MyBoathouse where ...• projection by superclassing

class SUPERCLASS a => SUBCLASS a• transformation by theory morphisms

instance BOATHOUSE YourBoathouse where ...


Related to (and inspired by)

Algebraic semiotics [Goguen] Blendings [Turner and Fauconnier] Frame semantics [Filmore] Attempts at extracting relations from

WordNet glosses [several authors]


Future work

Develop set of foundational relations for geospatial semantics• validate with other case studies

Apply to core ontological reasoning tasks• data discovery• service discovery• service composition• schema mapping

Translation to OWL ontologies in DOLCE


Conclusions

1. GIScience has a long and successful history of modeling interesting relations

2. We have left relations between types to non-spatial ontologists

3. There is something special about spatial in such relations: image schematic basis

4. Capture this by modeling types as theories in type classes of functional languages.


For more information...

MUSIL web site (Muenster Semantic Interoperability Lab):

http://musil.uni-muenster.de email to

[email protected]

http://musil.uni-muenster.de/





mailto:[email protected]




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GeoInfo 2005 GIScience and Relationships Werner Kuhn Muenster Semantic Interoperability Lab (MUSIL)

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