Foundations of Ontological Analysis

1. Foundations of Ontological Analysis Chris Welty, Vassar College

2. What is Ontology? • A discipline of Philosophy • Meta-physics dates back to Artistotle • Ontology dates back to 17th century • The science of what is • Borrowed by AI community • McCarthy (1980) calls for “a list of things that exist” • Evolution of meaning • Now refers to domain modeling, conceptual modeling, knowledge engineering, etc.

3. a set of general logical constraints a collection of taxonomies a catalog a glossary a set of text files a collection of frames a thesaurus complexity without automated reasoning with automated reasoning What is an Ontology?

4. Why Ontology? • “Semantic Interoperability” • Generalized database integration • Virtual Enterprises • e-commerce • Information Retrieval • Surface techniques hit barrier • Query answering over document sets • Natural Language Processing

5. Need more knowledge about what the user wants“Can the user please be more specific?” • Search for “Washington” (the person) • Google: 26,000,000 hits • 45th entry is the first relevant • Noise: places • Search for “George Washington” • Google: 2,200,00 hits • 3rd entry is relevant • Noise: institutions, other people, places

6. Solution Knowledge • Domain Knowledge • Person • George Washington • George Washington Carver • Place • Washington, D.C. • Artifact • George Washington Bridge • Organization • George Washington University • Semantic Markup of question and corpora • What Washington are you talking about?

7. Need more knowledge about the possible answers“Can the user please put more of the answer in the question?” • Search for “Artificial Intelligence Research” • Misses subfields of the general field • Misses references to “AI” and “Machine Intelligence” (synonyms) • Noise: non-research pages, other fields, Mensa types

8. Solution Knowledge • Domain Knowledge • Sub-fields (of AI) • Knowledge Representation • Machine Vision etc. • Neural networks • Synonyms (for AI) • Artificial Intelligence • Machine Intelligence • Query Expansion • Add disjuncted “general terms” to search • Add disjuncted “synonyms” to search • Semantic Markup of question and corpora • Add “general terms” (categories) • Add “synonyms”

9. Allies of my enemies are my…? • What are all the enemies of Iraq in the Persian Gulf according to the CIA World Fact Book? • “Persian Gulf” appears as a region and a body of water. • Misses: allies of enemies • Noise: countries with interests in the Persian Gulf, companies, ships, oil platforms

10. Solution: Knowledge + Reasoning(Cycorp/SRI HPKB) • Some axioms • Enemy of a country is a country • Ally of an enemy is an enemy • Enemy is reflexive • Countries are located in regions • Reformulate •  (country   located-in . (region  name = “Persian Gulf”)  enemy . (country  name = “Iraq”))

11. Solution Theme: More KnowledgeOntologies - at least part of the solution • “more semantics”, “richer knowledge” … ontologies • Idealized view • Knowledge-enabled search engines act as virtual librarians • Determine what you “really mean” • Discover relevant sources • Find what you “really want” • Requires common knowledge on all ends • Semantic linkage between questioning agent, answering agent and knowledge sources • Hence the “Semantic Web”

12. Key Challenges • Must build/design, analyze/evaluate, maintain/extend, and integrate/reconcile ontologies • Little guidance on how to do this • In spite of the pursuit of many syntactic standards • Where do we start when building an ontology? • What criteria do we use to evaluate ontologies? • How are ontologies extended? • How are different ontological choices reconciled? • Ontological Modeling and Analysis • Does your model mean what you intend? • Will it produce the right answers?

13. Contributions • Methodology to help analyze & build consistent ontologies • Formal foundation of ontological analysis • Meta-properties for analysis • “Upper Level” distinctions • Standard set of upper-level concepts • Standardizing semantics of ontological relations • Common ontological modeling pitfalls • Misuse of intended semantics • Specific recent work focused on clarifying the subsumption (is-a, subclass) relation

14. Upper Level • Particulars • Concrete • Location, event, object, substance, … • Abstract • information, story, collection, … • Universals • Property (Class) • Relation • Subsumption (subclass), instantiation, constitution, composition (part)

15. Subsumption • The most pervasive relationship in ontologies • Influence of taxonomies and OO • AKA: Is-a, a-kind-of, specialization-of, subclass (Brachman, 1983) • “horse is a mammal” • Capitalizes on general knowledge • Helps deal with complexity, structure • Reduces requirement to acquire and represent redundant specifics • What does it mean?  x f(x) r(x) Every instance of the subclass is necessarily an instance of the superclass

16. Overloading Subsumption Common modeling pitfalls • Instantiation • Constitution • Composition • Disjunction • Polysemy

17. Instantiation (1) Does this ontology mean that My ThinkPadis aThinkPad Model? ThinkPad Model T21 Ooops… My ThinkPad (s# xx123) Question: What ThinkPad models do you sell? Answer should NOT include My ThinkPad -- nor yours.

18. Instantiation (2) Notebook Computer ThinkPad Model T Series model T 21 My ThinkPad (s# xx123)

19. Composition (1) Computer Disk Drive Memory Micro Drive Question: What Computers do you sell? Answer should NOT include Disk Drives or Memory.

20. Composition (2) Computer part-of Disk Drive Memory Micro Drive

21. Disjunction (1) has-part Computer Computer Part Disk Drive Memory Micro Drive has-part Flashcard-110 Camera-15 Unintended model: flashcard-110 is a computer-part

22. has-part Disk Drive  Memory  … Computer Disjunction (2)

23. Polysemy (1)(Mikrokosmos) Physical Object Abstract Entity Book ….. Question: How many books do you have on Hemingway? Answer: 5,000

24. Polysemy (2)(WordNet) Physical Object Abstract Entity Book Sense 1 Book Sense 2 Biography of Hemingway …..

25. Constitution (1)(WordNet) Entity Amount of Matter Physical Object Clay Metal Computer Question: What types of matter will conduct electricity? Answer should NOT include computers.

26. Constitution (2) Entity Physical Object Amount of Matter constituted Computer Metal Clay

27. Technical Conclusions • Subsumption is an overloaded relation • Influence of OO • Force fit of simple taxonomic structures • Leads to misuse of is-a semantics • Ontological Analysis • A collection of well-defined knowledge structuring relations • Methodology for their consistent application • Meta-Properties for ontological relations • Provide basis for disciplined ontological analysis

28. Applications of Methodology • Ontologyworks • Ontoweb • TICCA, WedODE, Galen, … • Strong interest from and participation in • Semantic web (w3c) • IEEE SUO • Wordnet • Lexical resources

29. New opportunities • Principled and rigorous upper level • All extensions are affected by a poor upper-level • Restructuring of WordNet nouns • Restructuring of CYC upper level • Softer lower levels • Trade off speed and flexibility of statistical approaches • ML and IR techniques for ontology seeding • Query answering • confidence levels • explanations

30. Foundations of Ontological Analysis Chris Welty, Vassar College

31. Ontological Properties • Identity • How are instances of a class distinguished from each other • Unity • How are all the parts of an instance isolated • Essence • Can a property change over time • Dependence • Can an entity exist without some others

32. Example - Identity • Is time-interval a subclass of time-duration? • Initial answer: yes • IC for time-duration • Same-length • IC for time-interval • Same start & end occurrent time-duration time-interval

33. Example - Identity occurrent time-duration time-interval One hour 2-3 PM Tues. 3-4 PM Weds.

34. Guidelines • Examples of how to use meta properties • Automated system for checking constraints • Formalizing and standardizing semantics of ontology structuring relations • Examples of how to use upper level • Cataloguing common pitfalls • Early work has focused on subsumption

35. Meta Properties • Properties of properties • Fully formalized • Carries identity criteria • Carries unity criteria • Rigid • Dependent

36. Example - Rigidity

37. Approach • Draw fundamental notions from Formal Ontology • Establish a set of useful meta-properties, based on behavior wrt above notions • Explore the way these meta-properties combine to form relevant property kinds • Explore the taxonomic constraints imposed by these property kinds.

38. Basic Philosophical Notions(taken from Formal Ontology) • Essence • Identity • Unity • Dependence

39. Essence and Rigidity • Certain entities have essential properties. • Hammers must be hard. • John must be a person. • Certain properties are essential to all their instances (compare being a person with being hard). • These properties are rigid - if an entity is ever an instance of a rigid property, it must always be.

40. Formal Rigidity • f is rigid (+R): x f(x) f(x) • e.g. Person, Apple • f is non-rigid (-R): xf(x)  ¬f(x) • e.g. Red, Male • f is anti-rigid (~R): x f(x)  ¬f(x) • e.g. Student, Agent

41. Rigidity Constraint +R  ~R • Why?  x P(x) Q(x) Q~R P+R O10

42. Identity and Unity • Identity: is this my dog? • Unity: is the collar part of my dog?

43. Identity criteria • Classical formulation: f(x)f(y)  (r(x,y) x = y) • Generalization: f(x,t)f(y,t’)  (G(x,y,t,t’) x = y) (synchronic: t= t’ ; diachronic: t≠ t’) • In most cases, G is based on the sameness of certain characteristic features: G(x,y, t,t’)= z (c(x,z,t) c(y,z,t’))

44. A Stronger Notion:Global ICs • Local IC:f(x,t)f(y,t’)  (G(x,y,t,t’) x = y) • Global IC (rigid properties only): f(x,t) (f(y,t’) G(x,y,t,t’) x = y)

45. Identity Conditions along Taxonomies • Adding ICs: • Polygon: same edges, same angles • Triangle: two edges, one angle • Equilateral triangle: one edge • Just inheriting ICs: • Person • Student

46. Identity meta-properties • Supplying (global) identity (+O) • Having some “own” IC that doesn’t hold for a subsuming property • Carrying (global) identity (+I) • Having an IC (either own or inherited) • Not carrying(global) identity (-I)

47. Identity Disjointness Constraint Besides being used for recognizing sortals, ICs impose constraints on them, making their ontological nature explicit: Properties with incompatible ICs are disjoint • Examples: • sets vs. ordered sets • amounts of matter vs. assemblies

48. Unity Criteria • An object xis a whole under w iff w is an equivalence relation that binds together all the parts of x, such that P(y,x)  (P(z,x)  w(y,z)) but not w(y,z)  x(P(y,x)  P(z,x)) • P is the part-of relation •  can be seen as a generalized indirect connection

49. Unity Meta-Properties • If all instances of a property f are wholes under the samerelation, f carries unity (+U) • When at least one instance of f is not a whole, or when two instances of f are wholes under different relations, f does not carry unity (-U) • When no instance of f is a whole, f carries anti-unity (~U)

50. Unity Disjointness Constraint Properties with incompatible UCs are disjoint +U  ~U