Ontologies - What’s all the fuss about?

Lee McCluskey

Department of Computing and

Mathematical Sciences

University of Huddersfield

School of Computing and Mathematics, University of Huddersfield

Talk Outline

1. Definitions and Characteristics

2. Examples

3. Things for us to do?

+ references....

http://www.formalontology.it/Framing_first.htm

http://www.medg.lcs.mit.edu/top/ (“the ontology page”)

School of Computing and Mathematics, University of Huddersfield

Areas Related

Distributed AI, Expert Systems / KBS, Enterprise Models, Formal Requirements Specifications.. any explicit “Symbolic Knowledge Model”

Standards (“ designs for how components should behave when certain interactions occur”)

School of Computing and Mathematics, University of Huddersfield

Jargon - Origins from Philosophy

ONTOLOGY - “The systematic study of existence”

“the science or study of being”

EPISTEMOLOGY - “The study of knowledge”

School of Computing and Mathematics, University of Huddersfield

Jargon - AI/KBS Definitions

Tom Gruber’s (1992) page seems to be authorativehttp://www-ksl.stanford.edu/kst/what-is-an-ontology.html

yet it contains MANY definitions.. an ontology is:

-a specification of a conceptualization.

(A conceptualization is “an abstract, simplified view of the world”)

-a description .. of the concepts and relationships that can exist for an agent or a community of agents.

School of Computing and Mathematics, University of Huddersfield

Jargon - More Definitions-a specification used for making ontological

commitments

(Ontological commitments are agreements to use the shared vocabulary in a coherent and consistent manner)

-a declarative (explicit) specification of

all the “entities” = the set of all representational terms in a KBS

- Class/Subclass Taxonomy ... Or Object Schema..

Re-usable Domain Theory .. Spec of a Vocabulary

School of Computing and Mathematics, University of Huddersfield

Main Motivations

An ONTOLOGY is what you need to enable Knowledge Sharing and Re-use. It is at the heart of DAI. For this we may need to make an ontology PORTABLE - e.g. surrounding it with translation tools

An ONTOLOGY can be thought of as generally required extra vocabulary on top of FOL.

Fikes says KR Language = Logic + Ontology

School of Computing and Mathematics, University of Huddersfield

KIF is a language used for Expressing Ontologies (from R.Fikes’s slides, KR 96)

KIF (knowledge Interchange Format) -Lisp style predicate calculus. Ontologies using KIF:

(1) axiom sets that define Numbers, Lists and Sets (....!!)

(2) Ontolingua is an ontology that contains axioms defining FRAMES (classes and instances, slots and slot constraints)

(3) CML - a “Device Modelling Ontology”

School of Computing and Mathematics, University of Huddersfield

Kinds of OntologiesSo there seems to be two “kinds” of ontology:

“REPRESENTATION ONTOLOGY”

1. axiomatization of “extra baggage” that KR languages need to be expressive e.g. Is_a relations, sets and other maths data structures.

“APPLICATION ONTOLOGY”

2. “domain specific” ontologies - terms more related to a particular domain of application

School of Computing and Mathematics, University of Huddersfield

An attempt at a formal definition! BUT we NEED a quick excursion to Herbrand

Models, I think...

Consider a FOL language L, and a set of clauses within L called P.

EXAMPLE: L has constants a,b,predicates p,q and function f.

P is the following 4 clauses:

p(a). q(a). q(b). p(f(X)) <- p(X).

School of Computing and Mathematics, University of Huddersfield

Formal definition - 2

The Herbrand universe UL is the set of all ground terms of L

The Herbrand Base BL is the set of all ground atoms of L

A Herbrand Interpretation is a subset of BL

All Herbrand interpretations = set IL

(which forms a complete lattice under inclusion! Good for fixpoint theory..)

School of Computing and Mathematics, University of Huddersfield

Formal definition - 3

A Herbrand Model MP of a set of CLAUSES P written in L is a Herbrand interpretation which contains all logical consequences of P.

Back to Example:

{p(a), q(a), q(b), p(f(a)), p(f(f(a))), p(f(f(f(a))), ...}

is a (minimal) HM of our example clauses.

School of Computing and Mathematics, University of Huddersfield

Formal definition - 4

The “intended meaning” of a clause set P is the set M of ground facts that the user expects to be logical consequences of the clauses.

P is correct if HP is a subset of M

P is complete if M is a subset of HP

School of Computing and Mathematics, University of Huddersfield

Formal definition - 5 father(john,peter).

father(john,mary).

mother(mary,mike).

grandfather(X,Y)

<= father(X,Z), father(Z,Y).

... is correct but incomplete given the obvious intended meaning.

School of Computing and Mathematics, University of Huddersfield

Finally .. Guarino’s formal definition (‘96)(slightly adapted by TLM, ‘01)

Given logic language L, LET...

A conceptualisation be a set of models of L which describe the intended interpretations of L’s atoms.

Then...

An Ontology is a (possibly incomplete) “axiomatization” of a conceptualisation

School of Computing and Mathematics, University of Huddersfield

Back to Pragmatic aspects of Ontologies: What’s Special about Them...Emphasis on ..persistent properties .. “static” rather than

dynamic knowledge ..classes and class hierarchy ..collaborative development

“Ontologies are distinguished NOT by their form but by the role they play in representing knowledge” R. Fikes

School of Computing and Mathematics, University of Huddersfield

Example: The Conflict Prediction Specification

00's of definitional axioms in sorted FOL

00's of definitions in sorted, enriched FOL e.g.

"(FL 1000 is_the_max_flight_level_for Shanwick airspace)".

"the_segment_exit_long_Val_in_arc_mins_for(Linear_track_pt) = the_exit_long_Val_in_arc_mins_of(the_Segment_of(Linear_track_pt))".

School of Computing and Mathematics, University of Huddersfield

Example: Conflict Prediction Specification-- 00's of grammar rules defining a

Vocabulary

-- Definitional axioms are grounded in operators and objects from Sorts, and "built-in" arithmetic ops.

e.g. here's a low level axiom"(Time is_during_time_period_of Segment) <=>

[(Time is_at_or_later_than the_entry_Time_of(Segment)) & (Time is_at_or_earlier_than the_exit_Time_of(Segment)) ]"

School of Computing and Mathematics, University of Huddersfield

Example: Conflict Prediction SpecificationIs the CPS an ontology??

YES:

-- is a logic + lots of extra well-defined syntax

-- contains persistent knowledge (does not change during problem solving)

-- could well be used for many ATC applications (except for very specific top level axioms)

NO:

-- has built in non-defined stuff (arithmetic bits)

School of Computing and Mathematics, University of Huddersfield

Conflict Prediction Specification: Conclusion

The "lower level" axioms and facts form a Domain Specific Ontology for Oceanic ATC.

Trying to develop, extend and use it as such might be a useful bit of R and D.

School of Computing and Mathematics, University of Huddersfield

Example: Planning Domain Models

YES..

-persistent actions representations

-persistent object classes / facts

NO..

-lots of dynamic facts

-lots IMPLICIT i.e. semantics of actions.

School of Computing and Mathematics, University of Huddersfield

Conclusion: Planning Domain Models

The persistent parts of a PDM could be thought of as an application ontology.

Perhaps we should provide first order axiomatizations of actions to deliver representation ontologies?

School of Computing and Mathematics, University of Huddersfield

Conclusion: Ontologies are KRs with the aim of

sharing/communicating/re-using large, persistent KBs

Also, their emphasis on specifying declaratively that which hitherto has been hidden (e.g. Superstructure of KRLs) is good.

KRL = Logic + Ontology

..remembering that “Ontology” can be very specific for a specific KRL.