1. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 1 Description Logics: Logic foundation of Semantic Web Semantic Web - Fall 2005 Computer Engineering Department Sharif University of Technology

2. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 2 2 Outline  First order logic and Models  Introduction to Description Logics  Reasoning on Description Logics

3. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 3 3 Prepositional Logic

4. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 4 4 Truth Tables

5. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 5 5 First Order Logic (FOL)

6. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 6 6 Models

7. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 7 7 Important Equivalences

8. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 8 8 Example of a model

9. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 9 9 Knowledge Representation with FOL

10. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 10 10 Knowledge Representation with FOL

11. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 11 11 What Are Description Logics?  A family of logic based Knowledge Representation formalisms Based on concepts and roles  Concepts are interpreted as sets of objects.  Roles are interpreted as binary relations between objects. Descendants of semantic networks and KL-ONE  Key features of DLs are: Formal semantics  Decidable fragments of FOL  Closely related to Propositional Modal & Dynamic Logics Provision of inference services  Sound and complete decision procedures for key problems  Implemented systems (highly optimised)  Trade-off between expressive power and computational complexity.

12. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 12 12

13. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 13 13 Description Logic Family  Particular languages mainly characterised by: Set of constructors for building complex concepts and roles from simpler ones. Set of axioms for asserting facts about concepts, roles and individuals. Simplest logic in this family is named AL Others are specified by adding some suffixes like U  NC : ALC ALCU …

14. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 14 14 Description logic AL

15. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 15 15 Fundamental Equivalences

16. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 16 16 Interpretation (model)

17. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 17 17 Example of a model

18. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 18 18 AL Constructors at Work

19. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 19 19 Additional Constructors (1)

20. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 20 20 Additional Constructors (2)

21. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 21 21  The “Happy Father” concept:  A person who has at most one child or has at least 3 children from which at least one of them is female. Some Examples

22. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 22 22 Some more examples! Π

23. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 23 23 Classes

24. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 24 24 Semantic Networks

25. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 25 25 Rule Constructors

26. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 26 26 Examples  Expressing what we stated in slides 9 and 10 with DL: There is a lecturer who teaches INFS4201 Guido teaches every course Bob teaches some courses

27. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 27 27 DL as fragments of Predicate Logic

28. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 28 28 Lisp like style for DL

29. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 29 29 Normal Forms

30. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 30 30 Representing Knowledge in DL

31. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 31 31 DL Architecture

32. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 32 32 Terminologies or TBoxes

33. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 33 33 Terminologies or Tboxes (cont.)

34. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 34 34 Reasoning about TBoxes

35. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 35 35 Reduction to Subsumption

36. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 36 36 Reduction to Unsatisfiability

37. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 37 37 Reducing Unsatisfiability

38. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 38 38 Inference services

39. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 39 39 Inference service: concept satisfiability

40. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 40 40 Inference services based on satisfiability

41. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 41 41 Inference service: concept subsumption

42. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 42 42 Concept examples

43. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 43 43 Example taxonomy

44. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 44 44 World description: ABox

45. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 45 45 ABox inference services

46. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 46 46 Abox inference services (cont.)

47. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 47 47 ABox example

48. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 48 48 TBox taxonomy plus individuals

49. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 49 49 Open world assumption

50. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 50 50 Reasoning Procedures

51. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 51 51 Structural Subsumption

52. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 52 52 Examples

53. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 53 53 Example (do it yourself !)

54. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 54 54 Tableaux  The Tableaux Algorithm is a decision procedure solving the problem of satisfiability.  If a formula is satisfiable, the procedure will constructively exhibit a model of the formula.  The basic idea is to incrementally build the model by looking at the formula, by decomposing it in a top/down fashion. The procedure exhaustively looks at all the possibilities, so that it can eventually prove that no model could be found for unsatisfiable formulas.

55. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 55 55 Tableaux Algorithm

56. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 56 56 Negation Normal Form

57. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 57 57 Completion Rules: the AND rule

58. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 58 58 The AND rule

59. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 59 59 The OR rule

60. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 60 60 The SOME rule

61. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 61 61 The FORALL rule

62. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 62 62 Clash

63. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 63 63 Completion rules for the logic ALC

64. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 64 64 Example inference

65. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 65 65 Example inference

66. Semantic web course – Computer Engineering Department – Sharif Univ. of Technology – Fall 2005 66 66 References  Chapters 1 and 2 of DLHB.