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1. ????????

2. ????????????

????:?? 2009?9?9????14:00-15:30 ????:???? 2009?9?12????10:00-11:30 ????:???? 2009?9?13????9:00-10:30 ------------------------------------------------------------ LarKC ?????? 2009?9?13????14:00-15:30

3. Outline

??,??????? ????????? ???????? ??

6. ???????????????? ????, ????????? ???????????

??,???????

7. ?????Logics and Sciences

??????????????????,????????????????????? ????????????????????,????????????? ??????????????????,?????????????????

8. ????????????Avoiding a Pervasive Misunderstanding on Logics

??????????????(normative)??,?????????(descriptive)??, ????,??????????????????????,????????????????????

10. ??????????

(??????)???????????,??????????; (??????)?????????,?????; (??????)??????????????,????????????; (??????):?????????,????????; (??????):????????????,???????

11. ??????????????

12. ?????“??”

????????,???????????????,??????????????????? ??????,???????????????????,??????????????,???????? ????! ??????????!??????????,?????? ????,????!

13. ?????

Thank i,j? ?[doj(a)] ? ? [doj(-a)] ? ?done(j,a) ?(Ui(?)> Ui(?)) ? (Uj (?)> Uj(?)). ??????????????? ???????????????????(utility)??????????

14. ?????

Thank i,j? ?[doj(a)] ? ? [doj(-a)] ? ? done(j,a) ?(Ui(?)> Ui(?)) ??????????????? ????????????????????

17. ??

??????????????? ????????????????????????????????? Gratitude i,j? ?[doi(a)] ? ? [doi(-a)] ? ? done(j,a) ? (U i(?)-U i(?))>Gi? (Uj(?)-Uj(?)) >Gj).

20. ???????

Thank i,j? ?[doj(a)] ? ? [doj(-a)] ? ? done(j,a) ??Ojdone(j,a) ? (Ui(?)> Ui(?)) ? (Ui(?)> Ui(?)) ???? ?? ??????????: 1) (???????):?????????; 2)(???????):??????????????; 3)(???????)??????????

21. ?????????

??????????: ?Thank i,j? ?? ([doj(a)] ? ? [doj(-a)] ? ? done(j,a)) V Ojdone(j,a) V? ( (Ui(?)> Ui(?)) ? (Ui(?)> Ui(?)) ) ??? ?? ??????????: 1) (???????):??????????; ?? 2)(???????):?????????????????; ?? 3)(?????)????????

22. ?????

???????????????,???????????????????? ?????????????,??????????,??????????? ??????????????????????? ??????????,????????????????????????

24. ?????

Thank i,j? ?Ki[doj(a)] ? ? Kj[doj(-a)] ? ? done(j,a) ??Ojdone(j,a) ?(Ui(?)> Ui(?)) ? (Ui(?)> Ui(?)) Ki : ????????(Logic of knowledge and belief) [doj(a)]: ????(Dynamic Logic) Ui(?)> Ui(?) : ????(Preference Logic) ?Oj done(j,a):????(Deontic Logic) ????(Propositional Logic) ??????(First Order Predicate Logic)

25. ??????

????????????? ?????????????????? ?????????????????????

26. ?????:?????

?????:????,????????? ???????:???????????: ?????? ????:?????:??????? ???????????????????????? ??????????????????:?????????????????? ????

29. ?????

Thank i,j? ?Ki[doj(a)] ? ? Kj[doj(-a)] ? ? done(j,a) ??Ojdone(j,a) ?(Ui(?)> Ui(?)) ? (Ui(?)> Ui(?)) Ki : ????????(Logic of knowledge and belief) [doj(a)]: ????(Dynamic Logic) Ui(?)> Ui(?) : ????(Preference Logic) ?Oj done(j,a):????(Deontic Logic) ????(Propositional Logic) ??????(First Order Predicate Logic)

30. ?????????

??(Syntax),?? (Semantics),? ??(Pragmatics) ????(Truth Conditions) ??(Model), ??(State), ?????(Possible Worlds) ??(Propositions)???(Modalities)

31. ??(Syntax)??? (Semantics)

??????????? p ?P => p ? L ?, ? ? L => ? ? ? , ? v ? ? L ??????????????????????? M |= ? ? ? iff M |= ? ?? M |= ?

32. ?????

? |= ? (??????) ????:? |= ? iff ???????M,M|= ???? ?????:? |= ? iff ???????M,M|= ??? ??: ? ? ?‘ |= ? ???‘ ??????

33. ??????????(monotonic reasoning and non-monotonic reasoning)

????: ? |= ? => ?‘ |= ? for any ?’ ?? ?????: ????????

34. ???????????

35. ???????Key features of an Ontology

?????Concept hierarchy, ??????concept subsumption ??????? InstanceOf Relation (Instances) ??????? PartOf Relation (property)

36. Why not other alternatives

?????? the first-order predicate logic ??? set theory ???? programming languages

37. ?????

??????????(Individual)??? ???????????????(Set of individuals) ?????????????? ???????????????

39. ???? Description Logic

Knowledge Base Tbox (schema) Abox (data) Man ´ Human u Male Happy-Father ´ Man u 9 has-child Female u … John : Happy-Father hJohn, Maryi : has-child Inference System Interface

40. Basic Description Logic: AL

Concept Expressions: A (atomic concept) ? (universal concept) ? (bottom concept) ? A (atomic negation) C ? D (intersection) ?R.C (value restriction) ?R.T (limited existential quantification) where A is a concept name, C and D are concept expressions, and R is a role expression

41. Family of AL language

C ? D (Union) ?R.C (Full Existential Quantification) ? C (Complement) Number restriction (? n R) (at least restriction) (? n R) (at most restriction) Qualified number restriction (? n R.C) (at least restriction) (? n R.C) (at most restriction) Transitive Role: R+ Inverse of Role: I Role Hierarchies R ?S: H

42. Examples

woman = person ? female man = person ? ?woman mother = woman ? ?hasChild.person father = man ? ?hasChild.person

43. Decidable Subset of First-Order Logic Equivalent to 3 Variable Fragment (Borgida 1996) Model theoretic semantics by mapping to abstract domain Provides Primitives for defining Conceptual Knowledge Concept Expressions (Formulas with 1 free variable) for describing Sets of Objects Boolean Operators: C?? D, C ? D, ?C Quantifiers: (?R.C), (?P.C) Cardinality Constraints: (= n R), (> n R), (< n R), (? n R), (? n R) Axioms define relations between concepts Subsumption: C ? D Equivalence: C ? D Disjointness: C ?? D ? ?

Description Logics

44. DL Semantics

Interpretation function extends to concept expressions in an obvious(ish) way, i.e.:

45. Example

whitehorse = horse ? white. color(white). whitehorse = horse ? ?hasColor. {white}. ??white?????(nominal) whitehorse = horse ? ?hasColor. {white} ? ? hasColor. {white}.

46. ??????Web Ontology Language (OWL)

OWL is built on top of RDF OWL is for processing information on the web OWL was designed to be interpreted by computers OWL was not designed for being read by people OWL is written in XML OWL is a web standard

47. Design Goals for OWL

48. Layered language

OWL Lite: Classification hierarchy Simple constraints OWL DL: Maximal expressiveness While maintaining tractability Standard formalisation OWL Full: Very high expressiveness Loosing tractability Non-standard formalisation All syntactic freedom of RDF(self-modifying) Syntactic layering Semantic layering Full DL Lite

52. OWL Example: animals

<?xml version="1.0"?><rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#" xmlns:owl="http://www.w3.org/2002/07/owl#" xmlns:dc="http://purl.org/dc/elements/1.1/" xml:base="http://wasp.cs.vu.nl/sekt/ontology/animal"> <owl:Ontology rdf:about=“animal"/><owl:Class rdf:ID="Eagle"> <rdfs:subClassOf><owl:Class rdf:about="#Bird"/> </rdfs:subClassOf></owl:Class><owl:Class rdf:ID="Animal"/> <owl:Class rdf:ID="Fly"><owl:disjointWith> <owl:Class rdf:about="#Penguin"/></owl:disjointWith> <rdfs:subClassOf rdf:resource="#Animal"/> </owl:Class><owl:Class rdf:ID="Bird"> <rdfs:subClassOf rdf:resource="#Fly"/> </owl:Class> <owl:Class rdf:ID="Penguin"> <rdfs:subClassOf rdf:resource="#Bird"/> <owl:disjointWith rdf:resource="#Fly"/> </owl:Class> </rdf:RDF>

54. ??????:DIG Interface

???????(The Description Logic Implementation Group) http://dl.kr.org/dig/?1999??? ?????????????????????,??OWL-DL???????????????????? ????HTTP?????SOAP???

55. DIG Interface

??TELL????????????????, ??ASK????DIG?????????? ??,?????????????????????

56. Concept Language

57. Tell Language

58. Example

59. Response

60. Ask Language

61. Example:Ask

62. Response Language

63. Example: Response

65. Relational Content Analysis

66. ???????

69. ?????

??????(Hybrid Logic)?????????:? Internal Disagrement? ????? http://www.cs.vu.nl/~wva/pub/HL.pdf

70. Questions and Discussions