Conceptual Modeling and Ontological Analysis

1. Conceptual Modeling and Ontological Analysis Nicola Guarino, LADSEB CNR,Italy Chris Welty, Vassar College, USA

2. Objectives • Introduce the notions of formal ontology from Philosophy • Present basic tools for ontology-driven conceptual analysis based on formal ontology • Explore some principled guidelines for using these tools • Discuss examples of using these guidelines and tools in practice

3. An Interdisciplinary Approach • Towards a unified Ontology-driven Modelling Methodology for databases, knowledge bases and OO-systems • Grounded in reality • Transparent to people • Rigorous • General • Based on • Logic • Philosophy • (Linguistics)

4. Ontology and ontologies

5. What is Ontology • The study of being qua being: the study of possible • The study of the natureof possible: ontology as the theory of distinctions among possibilia • The study of the most general characteristics that anything must have in order to count as a (certain kind of) being or entity.

6. Definitions • Ontology (capital “o”): • a philosophical discipline. • An ontology (lowercase “o”): • specific artifact designed with the purpose of expressing the intended meaning of a vocabulary

7. What is an ontology? • A shared vocabulary • Plus … A specification (actually, a characterization) of the intended meaningof that vocabulary ...i.e., an ontology accounts for the commitment of a language to a certain conceptualization “An ontology is a specification of a conceptualization” [Gruber 95]

8. Models and Conceptualizations

9. Capturing Intended Meaning • First order logic is ontologically neutral • Logical KBs often rely on natural language to convey intended meaning

10. Models M(L) Intended models IK(L) Intended Models An ontology consisting of just a vocabulary is of little use - Unintended interpretationsneed to be excluded

11. Scene 1: blocks on a table What is a conceptualization? Conceptualization of scene 1: <{a, b, c, d, e }, {on, above, clear, table }>

12. Scene 2: a different arrangement of blocks What is a conceptualization? The same conceptualization?

13. apple LE same conceptualization mela LI What is a conceptualization • Conceptualization: the formal structure of reality as perceived and organized by an agent, independently of: • the vocabulary used (i.e., the language used) • the actual occurence of a specific situation • Different situations involving the same objects, described by different vocabularies, may share the same conceptualization.

14. Relations vs. Conceptual Relations (Montague-style semantics) ordinary relations are defined on a domain D: conceptual relations are defined on a domain space<D, W>

15. Intended models IK(L) Ontology Ontologies constrainthe intended meaning Conceptualization C Commitment K=<C,I> Language L Models M(L)

16. Levels of Ontological Depth • Lexicon • Vocabulary with NL definitions • Simple Taxonomy • Thesaurus • Taxonomy plus related-terms • Relational Model • Unconstrained use of arbitrary relations • Fully Axiomatized Theory

17. Our Framework: Ontology-DrivenConceptual Modeling

18. Formal Ontology • Theory of formal distinctionsand connectionswithin: • entities of the world, as we perceive it (particulars) • categories we use to talk about such entities (universals) • Basic tools of formal ontological analysis: • Theory of Parts and Wholes (Mereology) • Theory of Identity, Integrity, Essence • Theory of Dependence • Why formal? • Two meanings : • rigorous • general • Formal logic: connections between truths - neutral wrt truth • Formal ontology: connections between things - neutral wrt reality[Varzi 96] • Goal:characterizing particulars and universals by means of formal properties and relations.

19. Approach • Draw fundamental notions from Formal Ontology • Establish a set of useful property kinds, based on behavior wrt above notions (meta-properties). • Explore the constraints they impose on Information Systems design, and add further modeling principles • Establish a minimal top-level ontology to drive conceptual modeling

20. Framework Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations

21. A KB includes both From Ontology to Data • Reference ontology (development time) • establishes consensusabout meaning of terms • Application ontology (development time) • Focuses on a particular application • limited by relevance choices related to a certain application • Conceptual model (run time) • implements an ontology (Tbox) • Describes constraints between terms to be checked at run time (terminological services) • limited by expressive power of implementation medium • Database (Abox) (run time) • Describes a specific (epistemic) state of affairs

22. Formal Ontological Analysis • Mereology • Identity, Unity, Essence • Dependence

23. Mereology

24. supplementation:PPxy z ( PPzy  ¬ z=x) • principle of sum: z ( PPxz  PPyz  ¬  w(PPwz  ¬ (Pwx  Pwy))) • extensionality: x = y  (Pwx  Pwy) Excluded models: Mereology • A possible primitive: proper part-ofrelation (PP) • asymmetric • transitive • Pxy =def PPxy  x=y • Some further axioms:

25. The problems withGeneral Extensional Mereology • Generality of mereological sums • Extensionality • different identifying properties while having the same parts • different parts while having the same identifying properties • Admittability of atoms

26. a + b Stack#1 K b D a b a a b Stack#1 Part, Constitution, and Identity • Structuremay change identity • Extensionality is lost • Constitutionlinks the two entities • Constitution isasymmetric(implies dependence) a + b

27. Identity, Unity, Essence

28. Framework Conceptual Model Conceptualization Ontology User Methodology Minimal Top-Level Ontology Ontology-Driven Modeling Principles Useful Property Kinds Formal Ontological Properties/Relations 

29. Identity, Rigidity, Unity • How can an entity change while keeping its identity? • Under what conditions does an entity lose its identity? • Do entities have any essential properties? • Does a change of parts affect identity? • When does an entity count as one? ...How do we know the answers…

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

31. Essence and rigidity

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

33. 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

34. Identity and identity criteria

35. Synchronic Identity Criteria • Material objects: same-location • Immaterial objects: same-location not valid any more...

36. Diachronic Identity • Requires some notion of persistence • In addition, the sameness (or continuity) of certain properties is required • The castle/bunch of bricks • Identity is not similarity

37. A priori identity? Ultimately, identity criteria are the result ofour conceptualization of reality. They are always related to a classof entities considered as relevant for our purposes. In general, identitycan’t be defined. What we can have are just informative constraints.

38. Identity criteria • Based on the sameness of a certain propertyf(x,t)f(y,t’)  ((c(x,z,t) c(y,z,t’))x = y) • t= t’: synchronic; t≠ t’: diachronic • Generalization: f(x,t)f(y,t’) (G(x,y, t,t’)x = y)

39. Necessary ICs A formula G is a necessary IC for fif f(x,t)f(y,t’)  x=yG(x,y,t,t’) … provided that: • it is not equivalent to universal identity: ¬xytt’ G(x,y,t,t’)  x=y • it is not trivially true of all fs: ¬xytt’f(x,t)f(y,t’) G(x,y,t,t’)

40. Sufficient ICs A formula G is a sufficient IC of f if f(x,t)f(y,t’)  G(x,y,t,t’)x=y … provided that: • it is not equivalent to universal identity: ¬xytt’ G(x,y,t,t’)  x=y • itis not trivially false: xytt’ G(x,y,t,t’)

41. Identity Meta-Properties • Carrying Identity (+I) • Having an IC, either own or inherited. • Non-rigid properties must inherit ICs. • e.g. has-same-fingerprint an IC for Person • Supplying Identity (+O) • having an IC that is not carried by a subsuming property • Only Rigid properties can supply ICs

42. Local Identity? • Global IC: Rigid properties • Local IC (+L): non-Rigid properties • Local IC identifies instances of f only when they are instances of f • same-wing-pattern for Butterfly: • nec & suf but only when one entity is an instance of Butterfly, but not when that entity is a caterpillar • same-registration-no. for students • Only-suf: Holds only when one entity is in a certain “student experience” • Global IC identifies an entity for its entire existence (only for +R properties)

43. Unity and Unity Criteria

44. Unity Analysis • What counts as a whole? What makes it a whole? • In which sense are its parts connected? What are the properties of the connection relation? • How is the whole isolated from the background? What are its boundaries? • What is the role played by the parts with respect to the whole?

45. Unity analysisand Mereotopology • Primitive: topological connection(C) • Some axioms: • reflexivity • symmetry • monotonicity wrt parthood: Pxy  Cxz  Cyz • external contact: everything is connected with its mereological complement • Problems: • distinguish between open and closed regions? • get rid of P, defining Pxy =def Cxz  Cyz ? • different kinds of connection (line, point, surface): is C alone enough?

46. Unity Conditions • An object ais a whole under w iff w is an equivalence relation such that P(y,a)  P(z,a)  w(y,z) but not w(y,z)  x(P(y,x)  P(z,x)) •  can be seen as a generalized indirect connection

47. Conditions for Unity • To achieve this we need • a suitable connection relation - how do we get from one part to another? • some notion of boundary - how do we know when to stop?

48. Unity and Plurality* • Strong vs. weak self-connection • Piece of coal vs. lump of coal • Basic component vs. assembly • Surface connection vs. line or point connection • Singular objects: strongly self-connected (may be wholes or not) • Plural objects: sums of wholes • Collections (the sum is not a whole) • Plural wholes (the sum is also a whole) • Mere sums

49. Unity Meta-Properties • If all instances of a property f are wholes under the same relation, 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. Disjointness Theorem Properties with incompatible IC/UC are disjoint