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A Tutorial Summary of Description Logic and Hybrid Rules

A Tutorial Summary of Description Logic and Hybrid Rules. Jing Mei, Harold Boley October, 2005. a. R(a,b). b. Description Logics. d. R(a,d). DL: Family of (decidable) sublanguages of First-Order Logic Concept Atomic concepts: C, C 1 , C 2 , D

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A Tutorial Summary of Description Logic and Hybrid Rules

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  1. A Tutorial Summary ofDescription LogicandHybrid Rules Jing Mei, Harold Boley October, 2005

  2. a R(a,b) b Description Logics d R(a,d) • DL: Family of (decidable) sublanguages of First-Order Logic • Concept • Atomic concepts: C, C1, C2, D • Boolean combinations: negation, intersection, union • Restrictions: existential, universal, number qualifications • Role • Atomic roles: R, S • Property: transitive, symmetric, functional, inverse-functional • Axiom • TBox: subsumption • ABox: assertion e R(a,e) a R(a,b) b

  3. Rules • Language • term: constant, variable, function symbol • atom: predicate symbol applied to terms • literal: atom + negative atom • extended literal: literal + negation as failure literal • Head  Body • Without function symbols in atoms H and Bi • Datalog: H B1 …  Bm • Datalog: H1 …  Hn B1 …  Bm • Datalog : H1 …  Hn [naf] B1 …  [naf] Bm • With function symbols in atoms H and Bi • Horn programs: H B1 …  Bm • Normal programs: H [naf] B1 …  [naf] Bm • Extended programs: H1 …  Hn [naf][neg] B1 …  [naf][neg] Bm

  4. Hybrid Knowledge Base • Hybrid KB: K = (S, R) • S: a finite set of DL axioms in the ontology language • R: a finite set of hybrid rules • Hybrid Rules:H  B1 …  Bm & Q1 …  Qn • H, Bi are ordinary atoms for rules • Qj are queries to the DL component S

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