Foundations of Ontological Analysis

1. Foundations of Ontological Analysis Chris Welty, Vassar College

2. Part I The Business Case

3. 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.

4. a set of general logical axioms 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?

5. 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

6. Need more knowledge of what terms meanSame term, different concept DB- DB- Manual Book Book “The old man and the sea” “Windows XP Service Guide” “The old man and the sea” “Windows XP Service Guide” Unintended models occur during integration

7. Solution Knowledge • DB-a • xy Book(x) author-of(y,x)Person(y) • xy Manual(x)  author-of(y,x)Company(y) • Better captures intended meaning • Prevents (this) unintended model • Allows better standardization

8. Need more knowledge of what terms meanLess expressive More expressive DB- DB- • Horse • Name • Age • Owner • Horse • Name • Age Name: Top Hat Owner: Billings Age: 3 Name: Top Hat/Billings Age: 3 The same object becomes two.

9. Solution Knowledge • DB-a • Identity Criteria: Same name • DB- • Identity Criteria: Same name and owner • Better captures intended meaning

10. 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

11. 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?

12. 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

13. 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”

14. Need more knowledge of reasoningAllies 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

15. 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”))

16. 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” • Knowledge-enabled web integrates standardized terms • Requires common knowledge on all ends • Semantic linkage between questioning agent, answering agent and knowledge sources, etc. • Hence the “Semantic Web”

17. 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?

18. Most ontology efforts fail • Why? • The quality of the ontology dictates its impact • Poor ontology, poor results • Ontologies are built by people • …The average IQ is 100

19. 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

20. Upper LevelWhere do I start? • Particulars • Concrete • Location, event, object, substance, … • Abstract • information, story, collection, … • Universals • Property (Class) • Relation • Subsumption (subclass), instantiation, constitution, composition (part)

21. 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

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

23. 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.

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

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

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

27. 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

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

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

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

31. 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.

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

33. 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

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

35. Part II Formalization

36. 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.

37. Basic Philosophical Notions(taken from Formal Ontology) • 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

38. 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.

39. 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

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

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

42. 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’))

43. 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)

44. 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

45. 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)

46. 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

47. 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

48. 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)

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

50. Property Dependence • Does a property holding for x depend on something else besides x? (property dependence) • P(x)  y Q(y) • y should not be a part of x • Example: Student/Teacher, customer/vendor