???????? Logical Foundation of the Semantic Web

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???????? Logical Foundation of the Semantic Web
?? ??? Zhisheng Huang Vrije University
Amsterdam, The Netherlands huang_at_cs.vu.nl ?? ??
Wei Hu Southeast University whu_at_seu.edu.cn
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??????WWW and Logics
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???????????
???????????
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??????? Methodological Studies of Teaching

• ??????
• ??????
• ??????
• ??????

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?????Schedule
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CSWS09 ??Tutorials of CSWS09

• 8?29? ???
• 0900-1200 ??1Introduction to the Semantic
  Web(Ivan Herman)
• 1400-1530 ??2Semantic Web Rule Languages
  (Jeff Z. Pan)
• 1600-1730 ??3???????????????(??? )

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???????

• ?????
• ?????
• ??????????
• ????????????
• ??????????
• ??????????????????

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???????

• ?????
• ?????
• ??????????
• ????????????
• ????????????
• ??????????????????

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??1??????Lecture 1 Introduction to Modern
Logics

• ??????
• ????
• ?????????
• ??????

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?????Logics and Sciences

• ??????????????????,?????????????????????
• ????????????????????,?????????????
• ??????????????????,?????????????????

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????????????Avoiding a Pervasive
Misunderstanding on Logics

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

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?????Logics and Culture

• ?????????????????
• ??????????????????????????
• ????????????????
• ?????????????????
• ??????????????????
• ?????????????????????????????

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?????????? Differences between Eastern and
Western Ways of Thinking

• ??? ? ???(Synthetic vs Analytic )
• ???????(Holism vs Reductionism)
• ??? ? ??? (Fuzzy vs Crisp)
• ??? ? ??? (Pragmatic vs Descriptive)
• ??? ? ??? (Dynamic vs Static)

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??????????

• (??????)???????????,??????????
• (??????)?????????,?????
• (??????)??????????????,????????????
• (??????)?????????,????????
• (??????)????????????,???????

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????????

• ?????????????
• ??????????????????
• ??????????????
• ???????????

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?????????

• ???????
• ??, ?????
• ?????????
• ???
• ???
• ???
• ????????????????
• ????????????????

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????????

• ????Socrates(469 BC399 BC)
• ???Plato (428 BC 348 BC)
• ?????Aristotle (384 BC 322 BC)
• ????Euclid (325BC 265BC)

Aristotle
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???????

• ????????????????
• ????????????????
• ?????????
• ??????
• ????????
• ???????,
• ???

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???????????

• ????(1632-1677)(?)???
• ???(1596-1650)(?)???????
• ??(1643-1727)(?)????
• ?? (1872-1970) (?)????

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????

• ????(proposition logic)
• ??????(first-order predicate logics)
• ????(higher order logics)
• ????(probability logics)

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?????????

• ???(True and False)????(Boolean logic,????)
• ????(Primitive proposition)
• ????(Composite proposition)
• ????(Negation)
• ????(Conjunction)
• ????(Disjunction)
• ?????(Conditional)

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?????????

• ??, ?????(Individual, Function, and Predicate)
• ??(Quantifier)
• ?????(Universal Quantifier)
• ???? ? (Existantial Quantifier)

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

• ???(soundness)?????????????
• ???(completeness)?????????????

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?????????

• ???(1931)???????????,??????????????,??????,???????
  ??????????????????????.

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??????????????????Why not fuzzy logics

• ???????? f(p)0,1
• ???????
• ??????????f(-p) 1-f(p)?
• ???????????????f(pq)min(f(p),f(q))?
• f(pVq)max(f(p),f(q))?
• ?? f(pV-p)max(f(p),1-f(p))

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

• ?????????
• ???????????
• ?????????

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?????????

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

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??(Syntax)

• ???????????
• p ?P gt p ? L
• ?, ? ? L gt ?? , ? ? ? , ? v ? ? L

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????(Truth condition)

• ???????????????????????(????),
• ??,??????,??????
• M ? ? ? iff M ? ?? M ?

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??????(Possible World Semantics)

• ??????(Model)?????????????????????,??????????????
  ????????, ?p, r? ??????????,???????????(Possible
  World)

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??(State)

• ??(??)?????????,????????????, ????????????????????
  ?

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???????(World Lattice)
P, Q, R
Q, R
P, R
P, Q
Q
R
P
?
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??(Proposition)???(Modality)

• ??(Proposition)?????????????
• ??(Modality)?????????????

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?????

• ? ? (??????)
• ????? ? iff ???????M,M ????
• ?????? ? iff ???????M,M ???
• ?? ? ? ? ? ??? ??????

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

• ???? ? ? gt ? ? for any ? ??
• ????? ????????

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??????

• ????(Modal logics)
• ????(Temporal Logics)
• ????(Spatial Logics)
• ????(Deontic Logics)
• ????(Dynamic Logics)
• ????(Description Logics)
• ????(Epistemic Logics)
• ??????

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???? ?????

• ??(Syntax)
• p ?P gt p ? L,
• ?? L gt ?? ? L,
• ?? L gt ?? ? L(?????),
• ?, ? ? L gt ? ? ? ? L
• ??(Definition)
• ??df ? ??? (?????)
• v ? df ? ( ? ? ? ? ?)(????)
• ? ?? df ( ? ? v ?)(???)

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???? ????

• ????????L????????M(S, R, V)
• ??S????????
• R ?SXS ??????????
• V P -gt PowerSet(S)???????,???????????????????
• ?? ?????V?????P-gtS????

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???? ????

• M, s p iff s? V(p)
• M, s ?? iff M, s \ ?
• M, s ? ? ? iff M, s ? and M, s ?
• M, s ?? iff M, s ? for all s such that
  lts,sgt ? R
• ???s?????,???????s???????s????????

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???(Validity)

• ? is valid for a model M iff for any s, M,s ?
• ? is valid iff ? is valid for any model M

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??????

• Reflexive(???)if w R w, for every w in S
• Symmetric(???) if w R v implies v R w, for all w
  and v in S
• Transitive(????) if w R v and v R q together
  imply w R q, for all w,v, q in S.
• serial (???)if, for each w in S there is some v
  in S such that w R v.

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Normal Modal Logic
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Axioms
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Modal Logic Systems

• K  K N
• T  K T
• S4  T 4
• S5  S4 B
• D  K D.

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

• K  no conditions
• D  serial
• T  reflexive
• S4  reflexive and transitive
• S5  reflexive, symmetric and transitive

• ??????R is transitive
• ???? for all s, lts,sgt ?R (???)
• ??????

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????????

• ?????K(??), B(??)
• (K) K? ?K(? ??)?K ?
• (T) K? ? ?
• (4) K? ? KK?
• (???,?????????)
• (5) ?K? ? K?K ?
• (????,??????????)
• (D) ?B?

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

• ????(Logics of Causality)???????
• ??????
• ????(Logics of Preference)???????
• ??????

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???

• ?????????(???)????
• ?????? (?? , 1980)
• ????????????(???? c.470 BC - 399 BC)I know
  nothing except the fact of my ignorance
  --Socrates
• ????????

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?????????

• ??????????????
• ???????????
• ??????,?????????

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Questions and Discussions