A Tutorial Summary of Description Logic and Hybrid Rules Jing Mei, Harold Boley October, 2005

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

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

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