Ontology-Driven Conceptual Modeling with Applications

1. Ontology-Driven Conceptual Modeling with Applications Giancarlo Guizzardi (guizzardi@acm.org ) http://nemo.inf.ufes.br Computer Science Department Federal University of Espírito Santo (UFES), Brazil i* Internal Workshop Barcelona, Spain July, 2010

2. Prologue

3. What is Conceptual Modeling? • “the activity of formally describing some aspects of the physical and social world around us for purposes of understanding and communication…Conceptual modelling supports structuring and inferential facilities that are psychologically grounded. After all, the descriptions that arise from conceptual modelling activities are intended to be used by humans, not machines... The adequacy of a conceptual modelling notation rests on its contribution to the construction of models of reality that promote a common understanding of that reality among their human users.” John Mylopoulos

5. Formal Ontology • To uncover and analyze the general categories and principles that describe reality is the very business of philosophical Formal Ontology • Formal Ontology (Husserl): a discipline that deals with formal ontological structures (e.g. theory of parts, theory of wholes, types and instantiation, identity, dependence, unity) which apply to all material domains in reality.

6. What is Conceptual Modeling? • “the activity of formally describing some aspects of the physical and social world around us for purposes of understanding and communication…Conceptual modelling supports structuring and inferential facilities that are psychologically grounded. After all, the descriptions that arise from conceptual modelling activities are intended to be used by humans, not machines... The adequacy of a conceptual modelling notation rests on its contribution to the construction of models of reality that promote a common understanding of that reality among their human users.” John Mylopoulos

7. The Chomskian Hypothesis • I-Language vs. E-language • There is a universal common language competence (Universal Grammar/Mentalese) which is innate • There is a logical reason behind the fact that we are able to learn our first language, i.e., abstract a formal system capable of generating an infinite number of valid expressions: (i) only by being exposed to samples of this system; (ii) without meta-linguistic support which is available to second-language learners

9. Object types and taxonomic structures

10. General Terms and Common Nouns • (i) exaclty five mice were in the kitchen last night • (ii) the mouse which has eaten the cheese, has been in turn eaten by the cat

11. General Terms and Common Nouns • (i) exactly five X ... • (ii) the Y which is Z...

12. General Terms and Common Nouns • (i) exaclty five reds were in the kitchen last night • (ii) the red which has ..., has been in turn ...

13. General Terms and Common Nouns • Both reference and quantification require that the thing (or things) which are refered to or which form the domain of quantification are determinate individuals, i.e. their conditions for individuation and numerical identity must be determinate

14. Sortal and Characterizing Universals • Whilst the characterizing universals supply only a principle of application for the individuals they collect, sortal universals supply both a principle of application and a principle of identity

15. Foundations • (1) We can only make identity and identification statements with the support of a Sortal, i.e., the identity of an individual can only be traced in connection with a Sortal type, which provides a principle of individuation and identity to the particulars it collects (Gupta, Macnamara, Wiggins, Hirsch, Strawson) • Every Object in a conceptual model (CM) of the domain must be an instance of a CM-type representing a sortal.

16. Unique principle of Identity X • Y

17. X Unique principle of Identity • Y

18. Foundations • (2) An individual cannot obey incompatible principles of identity (Gupta, Macnamara, Wiggins, Hirsch, Strawson)

19. Distinctions Among Object Types {Insurable Item, Red} {Person, Apple}

21. Rigidity • A type T is rigid if for every instance x of T, x is necessarily (in the modal sense) an instance of T. In other words, if x instantiates T in a given world w, then x must instantiate T in every possible world w’: R(T) =def□(x T(x) □(T(x)))

22. Anti-Rigidity • A types T is anti-rigid if for every instance x of T, x is possibly (in the modal sense) not an instance of T. In other words, if x instantiates T in a given world w, then there is a possible world w’ in which x does not instantiate T: AR(T) =def□(x T(x) (T(x)))

23. Distinctions Among Object Types {Insurable Item} {Student, Teenager} {Person}

24. S … P P’ Foundations • (3) If an individual falls under two sortals in the course of its history there must be exactly one ultimate rigid sortal of which both sortals are specializations and from which they will inherit a principle of identity (Wiggins)

25. S … P P’ Restriction Principle • Instances of P and P’ must have obey a principle of identity (by 1) • The principles obeyed by the instances of P and P’ must be the same (by 2) (6) The common principle of identity cannot be supplied by P neither by P’

26. G … S … P P’ Uniqueness Principle (7) G and S cannot have incompatible principles of identity (by 2). Therefore, either: - G supplies the same principle as S and therefore G is the ultimate Sortal - G is does not supply any principle of identity (non-sortal)

27. Foundations • A Non-sortal type cannot have direct instances. • A Non-sortal type cannot appear in a conceptual model as a subtype of a sortal • An Object in a conceptual model of the domain cannot instantiate more than one ultimate Kind(substance sortal).

28. Distinctions Among Object Types {Insurable Item} {Student, Teenager} {Person} {Man, Woman}

31. Relational Dependence • A type T is relationally dependent on another type P via relation R iff for every instance x of T there is an instance y of P such that x and y are related via R: R(T,P,R) =def□(x T(x) y P(y)  R(x,y))

32. Distinctions Among Object Types {Insurable Item} {Student, Employee} {Teenager, Living Person} {Person}

36. A rigid type cannot be a subtype of a an anti-rigid type.

37. Student Person Subtyping with Rigid and Anti-Rigid Types • x Person(x)  □Person(x) • x Student(x)  Student(x) • □(Person(x)  Student(x)) • Person(John) • Student(John) • □Person(John) • □Student(John) • □Student(John)  Student(John)

38. Category of Type Supply Identity Carry Identity Rigidity Dependence SORTAL - + +/- +/- « kind » + + + - « subkind » - + + - « role » - + - + « phase » - + - - NON-SORTAL - - +/- +/- Different Categories of Types

39. Category of Type Supply Identity Identity Rigidity Dependence SORTAL - + +/- +/- « kind » + + + - « subkind » - + + - « role » - + - + « phase » - + - - NON-SORTAL - - +/~ +/- « category » - - + - « roleMixin » - - - + « mixin » - - ~ - Different Categories of Types

40. Distinctions Among Object Types {Customer} {Student, Employee} {Teenager, Living Person} {Person}

41. Roles with Disjoint Allowed Types

42. Roles with Disjoint Allowed Types

44. Roles with Disjoint Admissible Types

45. Roles with Disjoint Allowed Types

46. Roles with Disjoint Allowed Types

48. Roles with Disjoint Admissible Types

49. The Pattern in ORM by Terry Halpin

50. Category of Type Supply Identity Identity Rigidity Dependence SORTAL - + +/- +/- « kind » + + + - « subkind » - + + - « role » - + - + « phase » - + - - NON-SORTAL - - +/~ +/- « category » - - + - « roleMixin » - - - + « mixin » - - ~ - Different Categories of Types