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A Tutorial Summary of Description Logic and Hybrid Rules
Jing Mei, Harold Boley October, 2005
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Description Logics d R(a,d) b a R(a,b) 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
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Rules Language Head Body 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
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Hybrid Knowledge Base Hybrid Rules: H B1 … Bm & Q1 … Qn
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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