Evaluating Ontological Decisions with OntoClean

1. Evaluating Ontological Decisions with OntoClean Chris Welty, Vassar College, USA Nicola Guarino, LADSEB-CNR, Italy

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 • McCarthy calls for “a list of things that exist” • Evolution of meaning • Now refers to domain modelling, 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. OntoClean 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.

5. Dealing withOntologicalRelativism • Deciding about the meta-properties carried by a given property… Is up to YOU! • But a common agreementmust be achieved about the formal meaning (and practical utility) of meta-properties

6. What is a taxonomic relationship? • Is-a, a-kind-of, specialization-of, subclass (Brachman, 1983) • “horse is a mammal” • Helps deal with complexity • What does it mean?  x f(x) r(x)

7. Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations Ontology-driven conceptual modeling

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

9. 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.

10. 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

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

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

13. 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’))

14. 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)

15. 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

16. 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)

17. 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

18. 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

19. 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)

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

21. 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

22. Basic Property Kinds Table

23. Sortals, categories, and other properties • Sortals (horse, triangle, amount of matter, person, student...) • Carry identity • Usually correspond to nouns • High organizational utility • Main subclasses: types and roles • Categories (universal, particular, event, substance...) • No identity • Useful generalizations for sortals • Characterized by a set of (only necessary) formal properties • Good organizational utility • Other non-sortals (red, big, decomposable, eatable, dependent, singular...) • No identity • Correspond to adjectives • Span across different sortals • Limited organizational utility (but high semantic value)

24. A formal ontology of properties Category +R Non-sortal -I Attribution -R-D Role ~R+D Formal Role Property Material role Anti-rigid ~R Non-rigid -R Phased sortal -D +L Mixin -D Sortal+I Type +O Rigid +R Quasi-type -O

25. The Backbone Taxonomy Assumption: no entity without identity • Since identity is supplied by types, every entity must instantiate a type • The taxonomy of types spans the whole domain • Together with categories, types form the backbone taxonomy, which represents the invariant structure of a domain (rigid properties spanning the whole domain)

26. +R  ~R -I  +I -U  +U +U  ~U -D  +D Incompatible IC’s are disjoint Incompatible UC’s are disjoint Taxonomic Constraints • Categories subsume everything • Roles can’t subsume types

27. Idealized view of an ontology

28. An extended example

29. Dealing withOntologicalRelativism • Deciding about the meta-properties carried by a given property… Is up to YOU! • But a common agreementmust be achieved about the formal meaning (and practical utility) of meta-properties

30. Amount of matter Location Group Agent Red Physical object Living being Group of people Food Fruit Animal Legal agent Apple Vertebrate Caterpillar Red apple Butterfly Country Person Entity assign meta-properties Social entity Organization

31. Entity-I-U-D+R Remove non-rigid properties Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Agent -I-U+D~R Red -I-U-D-R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Food +I-O~U+D~R Fruit +O+U-D+R Animal +O+U-D+R Legal agent +L-U+D~R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Red apple +I-O+U-D~R Country +L+U-D~R Person +O+U-D+R

32. Entity-I-U-D+R Analyze taxonomic links Amount of matter +O~U-D+R Location +O-U-D+R • ~U can’t subsume +U • Living being can change parts and remain the same, but amounts of matter can not (incompatible ICs) • Living being is constituted of matter Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R

33. Entity-I-U-D+R Analyze taxonomic links Amount of matter +O~U-D+R Location +O-U-D+R • ~U can’t subsume +U • Living being can change parts and remain the same, but amounts of matter can not (incompatible ICs) • Living being is constituted of matter Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R

34. Entity-I-U-D+R Analyze taxonomic links Amount of matter +O~U-D+R Location +O-U-D+R • ~U can’t subsume +U • Physical objects can change parts and remain the same, but amounts of matter can not (incompatible ICs) • Physical object is constituted of matter Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R

35. Entity-I-U-D+R Analyze taxonomic links Amount of matter +O~U-D+R Location +O-U-D+R • ~U can’t subsume +U • Physical objects can change parts and remain the same, but amounts of matter can not (incompatible ICs) • Physical object is constituted of matter Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R

36. Entity-I-U-D+R Analyze taxonomic links Amount of matter +O~U-D+R Location +O-U-D+R • Meta-properties fine • Identity-check fails: when an entity stops being an animal, it does not stop being a physical object (when an animal dies, its body remains) • Constitution again Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R

37. Entity-I-U-D+R Analyze taxonomic links Amount of matter +O~U-D+R Location +O-U-D+R • Meta-properties fine • Identity-check fails: when an entity stops being an animal, it does not stop being a physical object (when an animal dies, its body remains) • Constitution again Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R

38. Entity-I-U-D+R Analyze taxonomic links Amount of matter +O~U-D+R Location +O-U-D+R • ~U can’t subsume +U • A group, and group of people, can’t change parts - it becomes a different group • A social entity can change parts - it’s more than just a group (incompatible IC) • Constitution again Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R

39. Entity-I-U-D+R Analyze taxonomic links Amount of matter +O~U-D+R Location +O-U-D+R • ~U can’t subsume +U • A group, and group of people, can’t change parts - it becomes a different group • A social entity can change parts - it’s more than just a group (incompatible IC) • Constitution again Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Group of people +I-O~U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Apple +O+U-D+R Vertebrate +I-O+U-D+R Organization +O+U-D+R Person +O+U-D+R

40. Entity-I-U-D+R Agent -I-U+D~R Analyze Roles Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R • ~R can’t subsume +R • Really want a type restriction: all agents are animals or social entities. • Subsumption is not disjunction! Physical object +O+U-D+R Living being +O+U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

41. Entity-I-U-D+R Analyze Roles Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R • ~R can’t subsume +R • Really want a type restriction: all agents are animals or social entities. • Subsumption is not disjunction! Agent -I-U+D~R Physical object +O+U-D+R Living being +O+U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

42. Entity-I-U-D+R Legal agent +L-U+D~R Analyze Roles Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R • ~R can’t subsume +R • Another disjunction: all legal agents are countries, persons, or organizations Agent -I-U+D~R Physical object +O+U-D+R Living being +O+U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

43. Entity-I-U-D+R Analyze Roles Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R • ~R can’t subsume +R • Another disjunction: all legal agents are countries, persons, or organizations Agent -I-U+D~R Physical object +O+U-D+R Living being +O+U-D+R Legal agent +L-U+D~R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

44. Entity-I-U-D+R Food +I-O~U+D~R Analyze Roles Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Agent -I-U+D~R • ~R can’t subsume +R • Apple is not necessarily food. A poison-apple, e.g., is still an apple. • ~U can’t subsume +U • Caterpillars are wholes, food is stuff. Physical object +O+U-D+R Living being +O+U-D+R Legal agent +L-U+D~R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

45. Entity-I-U-D+R Analyze Roles Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Agent -I-U+D~R • ~R can’t subsume +R • Apple is not necessarily food. A poison-apple, e.g., is still an apple. • ~U can’t subsume +U • Caterpillars are wholes, food is stuff. Physical object +O+U-D+R Living being +O+U-D+R Legal agent +L-U+D~R Food +I-O~U+D~R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

46. Entity-I-U-D+R Red -I-U-D-R Red apple +I-O+U-D~R Analyze Attributions Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Agent -I-U+D~R • No violations • Attributions are discouraged, can be confusing. • Often better to use attribute values (i.e. Apple Color red) Physical object +O+U-D+R Living being +O+U-D+R Legal agent +L-U+D~R Food +I-O~U+D~R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

47. Entity-I-U-D+R Red -I-U-D-R Red apple +I-O+U-D~R Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Agent -I-U+D~R Physical object +O+U-D+R Living being +O+U-D+R Legal agent +L-U+D~R Food +I-O~U+D~R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Person +O+U-D+R Organization +O+U-D+R

48. Entity-I-U-D+R The backbone taxonomy Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Physical object +O+U-D+R Living being +O+U-D+R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Person +O+U-D+R Organization +O+U-D+R

49. Entity-I-U-D+R Amount of matter +O~U-D+R Location +O-U-D+R Group +O~U-D+R Agent -I-U+D~R Physical object +O+U-D+R Living being +O+U-D+R Legal agent +L-U+D~R Food +I-O~U+D~R Red -I-U-D-R Social entity -I+U-D+R Fruit +O+U-D+R Animal +O+U-D+R Group of people +I-O~U-D+R Apple +O+U-D+R Lepidopteran +O+U-D+R Vertebrate +I-O+U-D+R Geographical Region +O-U-D+R Country +O+U-D+R Caterpillar +L+U-D~R Butterfly +L+U-D~R Red apple +I-O+U-D~R Person +O+U-D+R Organization +O+U-D+R

50. Amount of matter Location Group Agent Red Physical object Living being Group of people Food Fruit Animal Legal agent Apple Vertebrate Caterpillar Red apple Butterfly Country Person Entity Before Social entity Organization