Some comments on Granularity Scale & Collectivity by Rector & Rogers

1. Some comments onGranularity Scale & Collectivityby Rector & Rogers Thomas Bittner IFOMIS Saarbruecken

2. Overview • Problems with doing ontology using DLs • Problems with collectives • Problems with indeterminacy • Problems with transitivity • Conclusions

3. Problems with doing ontology using Description Logics

4. We chose a language such that we can express the important aspects of the Bio-medical world Language L (symbols+meaning) This is what you actually say in your your ontology The biomedical domain is among the intended models = What you want to talk about What you could say in L = Models of the language L Ontologies constrain intended meaning The biomedical world

5. Ontologies constrain intended meaning The biomedical world Language L Models of the language L Intended models Ontology Guarino, 1998

6. Good Ontology Ontologies constrain intended meaning Guarino, 1998

7. Bad Ontology Very bad Ontology Ontologies constrain intended meaning Guarino, 1998

8. Bad Ontology • Mistakes when writing • axioms • Too few axioms Inappropriate tools which do not allow you to write good ontologies Ontologies constrain intended meaning

9. Kinds of Ontology Languages

10. Meaning specified implicitly and informally in natural language Kinds of Ontology Languages • A shared vocabulary plus a specification of its intended meaning Different degrees of expressive power for the specification of the intended meaning Two extremes

11. Meaning specified implicitly and informally in natural language meaning specified explicitly as a logical theory Kinds of Ontology Languages • A shared vocabulary plus a specification of its intended meaning Different degrees of rigor of the specification of the intended meaning Two extremes In between a continuum of degree of expressive power

12. Kinds of Ontology Languages ad hoc Hierarchies (Yahoo!) Description Logics (DAML+OIL) XML Schema structured Glossaries formal Taxonomies XML DTDs Terms Thesauri Data Models (UML, STEP) Principled, informalhierarchies ‘ordinary’ Glossaries Data Dictionaries (EDI) General Logic Frames (Protege) DB Schema Glossaries & Data Dictionaries Thesauri, Taxonomies MetaData, XML Schemas, & Data Models Formal Ontologies & Inference Michael Gruninger, gruning@nist.gov

13. Kinds of Ontology Languages ad hoc Hierarchies (Yahoo!) Description Logics (DAML+OIL) XML Schema structured Glossaries formal Taxonomies XML DTDs Terms Thesauri Data Models (UML, STEP) Principled, informalhierarchies ‘ordinary’ Glossaries Data Dictionaries (EDI) General Logic Frames (Protege) DB Schema Glossaries & Data Dictionaries Thesauri, Taxonomies MetaData, XML Schemas, & Data Models Formal Ontologies & Inference Michael Gruninger, gruning@nist.gov

14. Kinds of Ontology Languages ad hoc Hierarchies (Yahoo!) Description Logics (DAML+OIL) XML Schema structured Glossaries formal Taxonomies XML DTDs Terms Thesauri Data Models (UML, STEP) Principled, informalhierarchies ‘ordinary’ Glossaries Data Dictionaries (EDI) General Logic Frames Protege DB Schema Glossaries & Data Dictionaries Thesauri, Taxonomies MetaData, XML Schemas, & Data Models Formal Ontologies & Inference Michael Gruninger, gruning@nist.gov

15. Kinds of Ontology Languages ad hoc Hierarchies (Yahoo!) Description Logics (DAML+OIL) XML Schema structured Glossaries formal Taxonomies XML DTDs Terms Thesauri Data Models (UML, STEP) Principled, informalhierarchies ‘ordinary’ Glossaries Data Dictionaries (EDI) General Logic Frames Protege DB Schema Glossaries & Data Dictionaries Thesauri, Taxonomies MetaData, XML Schemas, & Data Models Formal Ontologies & Inference Michael Gruninger, gruning@nist.gov

16. Why do we need formulate ontologies in very expressive languages?

17. Good Ontology Why do we need formulate ontologies in expressive languages? It is the only way to produce good ontologies!!

18. Tradeoff between expressive power and computability How well can we specify intended meaning What can we compute automatically Kinds of Ontology Languages Description Logics (DAML+OIL) General Logic

19. Tradeoff between expressive power and computability Kinds of Ontology Languages Description Logics (DAML+OIL) General Logic How well can we specify intended meaning What can we compute automatically

20. Tradeoff between expressive power and computability Kinds of Ontology Languages Description Logics (DAML+OIL) General Logic How well can we specify intended meaning What can we compute automatically

21. We need BOTH kinds of languages Description Logics (DAML+OIL) Tradeoff between expressive power and computability General Logic How well can we specify intended meaning What can we compute automatically

22. Top Level Ontologies for arbitrary domains Endurant vs. perdurant (process) Parthood Constitution Ontologies

23. Top Level Ontologies for arbitrary domains Parthood Containment Constitution Computational ontologies and for specific domains GALEN FMA SNOMED Ontologies

24. Top Level Ontologies for arbitrary domains Parthood Containment Constitution Computational ontologies and for specific domains GALEN FMA SNOMED Focus on Class hierarchies Focus on RELATIONS and properties of relations Ontologies

25. Top Level Ontologies for arbitrary domains Computational ontologies and for specific domains Focus on Class hierarchies Focus on RELATIONS and properties of relations Requires high expressive power Requires limited Expressive power Ontologies

26. Top Level Ontologies for arbitrary domains Computational ontologies and for specific domains Focus on high expressive power Focus on computation Description logics are the right tools First order logic is the right language Ontologies

27. Top Level Ontologies for arbitrary domains Computational ontologies and for specific domains Alan and Jeremy use Description Logics to as tools to specify a top level ontology Ontologies

28. Problems with collectives

29. Object-like parts Skin tissue Skin The skin (an organ)

30. The organ ‘skin’ Collective of cells/ tissue Individual cell Skin tissue = collective of cells

31. Level of granularity X Entities of scale X Collectives of Entities of scale Y Level of granularity Y Entities of Scale Y Levels of granularity The organ ‘skin’ Collective of cells Individual cell

32. Entities are treated as individuals Level of granularity X Members of the Collection are NOT treated as individuals Level of granularity Y Levels of granularity Entities of scale X Collectives of Entities of scale Y Entities of Scale Y

33. Entities are treated as individuals Level of granularity X Members of the Collection are NOT treated as individuals Levels of granularity Entities of scale X Collectives of Entities of scale Y • Collectives must have MANY members • Cell/molecules/atoms/

34. We are interested in BIG collectives • In SMALL collectives we can individuate the members. • Problem: • The sum/union of two BIG collectives IS a BIG collection • The INTERSECTION of two BIG collectives is NOT necessarily a BIG collection • Parthood relation between BIG collectives CANNOT be modeled using the subset/subcollective relation

35. BIG BIG small The INTERSECTION of two BIG collectives is NOT necessarily a BIG collection

36. Weak supplementation principle does NOT hold Parthood relation between masses/collectives • is DIFFERENT from parthood between individual entities

37. Weak supplementation principle x proper-part-of y 

38. Weak supplementation principle x proper-part-of y  (z)(z proper-part-of y AND overlap zx)

39. Weak supplementation principle x proper-part-of y  (z)(z proper-part-of y AND overlap zx) Size of z does NOT matter

40. BIG collective small collective BIG collective Weak supplementation principle for big collectives x p-mass-part-of y  (z)(z p-mass-part-of y AND overlap zx)

41. You cannot make this distinction in a Description Logic The weak supplementation principle

42. Bad Ontology Ontology does not make enough distinctions Does NOT constrain meaning well enough Ontologies constrain intended meaning

43. This is always a bad justification!! Empty collectives • Empty collectives do not have grains/members • ‘Empty collectives are allowed. This is convenient …’ (Rector & Rogers)

44. Empty collectives • Empty collectives do not have grains/members • ‘Empty collectives are allowed. This is convenient …’ (Rector & Rogers) If we allow empty collectives then collectives are ABSTRACT entities

45. concrete concrete abstract abstract Empty collectives are abstract! • Abstract entities can be parts of concrete entities • Collective-of-blood-cells part-of blood Blood cell grain-of Collective-of-blood-cells

46. concrete concrete abstract abstract Blood cell part-of Collective-of-blood-cells Empty collectives are abstract! Blood cell grain-of Collective-of-blood-cells

47. concrete abstract Blood cell part-of Collective-of-blood-cells Empty collectives are abstract! • Abstract entities are immaterial and immaterial entities cannot have material parts • E.g., a hole CANNOT have a material part • So how can a blood cell be part of an ABSTRACTcollective of blood cells?

48. Bad Ontology Collectives are concrete Collectives are abstract Ontologies constrain intended meaning

49. Give up empty collectives Give up that is-grain-of is a parthood relation So how can a blood cell be part of a collective of blood cells? I suggest: Do BOTH!!

50. Problems with indeterminacy