Part-Whole Reasoning in Object-Centered Frameworks

1. Part-Whole Reasoning in Object-Centered Frameworks Patrick Lambrix Linköpings universitet

2. Outline • Databases • Knowledge representation - early approaches - description logics

3. Databases • Support for complex/composite objects one of the important requirements for object-oriented databases. - object-oriented database system manifesto, 1989 - third-generation database system manifesto, 1990.

4. Requirements for DatabasesSupporting Composite Objects • Object identity to which parts can be assigned. • Modeling of part-whole relations. • Derived values in wholes and parts. • Wholes can be manipulated as a whole. • Constraints on part-whole relations. • View composite objects at different levels. • Flexible transaction management.

5. ORION • Composite objects are classified with respect to: - dependent parts - exclusive / shared parts • Query facilities for traversing part-of hierarchy. • Clustering, authorization, locking.

6. Change propagation • Issue in several other OODBMSs Should changes in parts (always) be propagated to the whole? Should new versions of parts give rise to new versions of the whole?

7. Early approaches in knowledge representation • CSAW (1977) • Represent part-of • Dependence • NETL (1979) • Represent part-of, transitive • Transitive closure • Part-of hierarchy is integrated in semantic network

8. Early approaches in knowledge representation • Schubert (1979, 1981) • Represent part-of, partial ordering, object level • Extensionality • Unique empty part • Overlap, merging, difference operators • Parts graph based on partitions

9. lamp P P electrical system support structure stand top P P lamp shade socket bulb cord switch P cable plug

10. Part-whole reasoning in description logics

11. Part-whole reasoning in description logics • Conceptual modeling issues • P: A language for an engineering application (Sattler) • ALCS: quantifying over collections and parts (Franconi) • ’inheritance’ via part-of (Bernauer) • Reasoning services (Lambrix, Padgham & Shahmehri)

12. Conceptual modeling issues • Explicit introduction of wholes in the model • Clear distinction between parts and other attributes of a whole • Transitivity issues • Names of parts • Vertical and horizontal relationships

13. Implicit John: age: 35 sex: male wife: Mary Mary: age: 33 sex: female husband: John Explicit John: age: 35 sex: male Mary: age: 33 sex: female Mary-john-family: wife: Mary husband: John Explicit introduction of wholes in the model

14. Explicit introduction of wholes in the model • Reusability • Understandability • Extendibility

15. Clear distinction between parts and other attributes of a whole • Distinguish part attributes from other attributes • Needed for first-class status of part attributes (particular semantics, reasoning services)

16. Transitivity issues • PART-OF, transitive • Basic PART-OF, transitive Non-transitive sub-relations possible • Kinds of part-whole relations

17. Car(car1), wheel1 < car1 Wheel(wheel1) Car(car1) Has-wheel(car1,wheel1) Wheel(wheel1) Implicit assumption Has-wheel is a kind of part attribute Names of parts

18. Names of parts • Part attributes need to be tagged • Formal properties of PART-OF may not hold for sub-relations (e.g. transitivity) • Easy to specify particular characteristics (e.g. domain and cardinality restrictions)

19. Vertical and horizontal relationships • Vertical relationships • Dependence between the existence of the whole and the existence of parts (and vice versa) • Dependence between the properties of the whole and of the parts (and vice versa)

20. Vertical and horizontal relationships • Horizontal relationships • Constraints among parts that characterize the integrity of the whole

21. P: A language for an engineering application (Sattler)

22. Main ideas • Different kinds of part-whole relations • Inverses (whole-part relations) • Composition table of part relations • Specific interactions between parts and whole

23. Direct part-whole relations • Is-direct-component • Is-direct-member • Is-direct-segment • Is-direct-quantity • Is-direct-stuff • Is-direct-ingredient

24. Part-whole and whole-part relations • Part-whole relations: transitive closures of direct relations • Whole-part relations: Inverses of part-whole relations

25. Composition tables CC MC SE SO IO CC MC SE QM SO IO

26. Interactions between parts and whole • Exclusive parts: one of the direct part roles has at most one filler. Brain = (and (atmost 1 Is-direct-component Human) …) • Essential parts: existence of part is essential. Human = (and (exists (inv Is-direct-component) Brain) …)

27. Language • ALC + Inverse roles Role disjunction Role composition Transitive closure of roles Qualified number restrictions Role conjunction

28. ALCS: quantifying over collections and parts (Franconi)

29. Main ideas • Give semantics to plurals and plural quantifiers • Quantifiers for different plural readings The Beatles sing ’yesterday’.

30. Examples Location of connected parts of a stereo-system is the same as the location of the stereo-system. Stereo-system = (and (exists has-part remote-control) (exists (DR connected location) room) …) Remote-control = (and (not connected) … )

31. Language • ALC + PART-OF Satisfiability is a PSPACE-complete problem

32. ’inheritance’ via part-of (Bernauer)

33. Main ideas • Part-sensitive subsumption Based on taxonomy and partonomy • Part-of, transitive

34. Assumptions • Focus on medical domain • Mainly component/integral object and place/area • Transitivity across these types often acceptable

35. Approach • Explicit taxonomy for is-a and explicit partonomy for part-whole relations • PART-OF, transitive • 2 kinds of subsumption - ’ordinary’ subsumption - part-sensitive subsumption • Restricted language Concept: base concept + role restrictions

36. Reasoning services (Lambrix, Padgham & Shahmehri)

37. Main ideas • Named parts • Specialized constructs for parts • Horizontal (and vertical) constraints • Specialized reasoning services for part-of

38. Underlying model Underlying assumptions • Named direct parts: x is n-part of y • x is part of y iff there is a chain of named part relations between x and y • Axiom 1: object x is not part of x • Axiom 2: composite object has at least two parts • Axiom 3: if y is a direct part of x, then there is no other object z such that y is part of z and z is part of x

39. Underlying model Module: x is a module of y iff all parts of x are parts of y and y has also other parts Compositional inclusion: partial order based on part and module

40. Underlying model • No extensionialty • No principle of sum • Axiom 2 not checked for individuals

41. Terminological knowledge • Similar constructs for part relations as for roles • Specialized constructs • Horizontal and vertical constraints - relationships between parts - relationships between parts and whole • Modules

42. Terminological knowledge document = (and (atleast 1 supervisor) (atmost 1 supervisor) (atleastp 1 title-part) (atmostp 1 title-part) (allp title-part string) (atleastp 3 section-part) (allp section-part section) (allp reference-part reference) (order-constraint title-part section-part) (order-constraint section-part reference-part))

43. Supervisor (1,1) document reference-part (0,-) title-part (1,1) section-part (3,-) < < string section reference

44. Terminological knowledge standard-document = (and document (atleast 1 author) (atmost 1 author) (atmostp 3 section-part) )

45. Terminological knowledge • Horizontal constraints (pp-constraint married husband-part wife-part) (order-constraint title-part section-part) • Vertical constraints (same-filler item-part.item-number item-number) (aggregate location-part location-supervisor pick-space-supervisor)

46. Assertional knowledge • Similar constructs for part-relations as for roles • Part hierarchy (compositional inclusion)

47. Assertional knowledge d : (and document (part-fills title-part t) (part-fills section-part s1 s2 s3) (fills project-name dl-project) (fills supervisor John)) t: (and string (before s1 in d)) s1: (and section (before s2 in d)) s2: (and section (before s3 in d)) s3: section

48. dl-project project-name d john supervisor title-part section-part section-part section-part t s1 s2 s3 <(d) <(d) <(d)

49. Part hierarchy dl-project d john t s1 s2 s3

50. Reasoning service: composes Idea: when can a number of parts be used to compose a composite object of a given type • Parts need to belong to right concept • Order constraints are satisfied • Number of parts conforms to the given concept • No unnecessary parts • Explicitly required parts are present