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Ontologies - What’s all the fuss about?

Ontologies - What’s all the fuss about?. Lee McCluskey Department of Computing and Mathematical Sciences 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

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Ontologies - What’s all the fuss about?

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  1. Ontologies - What’s all the fuss about? Lee McCluskey Department of Computing and Mathematical Sciences University of Huddersfield

  2. 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”)

  3. 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”)

  4. Jargon - Origins from Philosophy ONTOLOGY - “The systematic study of existence” “the science or study of being” EPISTEMOLOGY - “The study of knowledge”

  5. Jargon - AI/KBS Definitions Tom Gruber’s (1992) page seems to be authorative http://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.

  6. 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

  7. 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

  8. 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”

  9. Kinds of Ontologies So 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

  10. 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).

  11. 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..)

  12. 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.

  13. 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

  14. 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.

  15. 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

  16. 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

  17. 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))".

  18. 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)) ]"

  19. Example: Conflict Prediction Specification Is 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)

  20. 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.

  21. Example: Planning Domain Models YES.. -persistent actions representations -persistent object classes / facts NO.. -lots of dynamic facts -lots IMPLICIT i.e. semantics of actions.

  22. 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?

  23. 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.

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