Using clausal deductive databases for defining semantics in disjunctive deductive databases

Abstract

This paper investigates the novel concept of i>clausal deductive databases (cd-databases), which are special normal deductive databases – i.e., deductive databases which may contain default negation in rule bodies – over a typed meta-language i>Lcd with a fixed set of predicate symbols, namely i>dis, i>con, and some i>built-in predicate symbols. The arguments of the literals in i>Lcd are given by disjunctive and conjunctive clauses of a basic first-order language l. i>Disjunctive deductive databases (dd-databases) generalize normal deductive databases by allowing for disjunctions of atoms or literals in rule heads. We present a i>transformation which maps a dd-database i>D into a cd-database i>Dcd that talks about the clauses of i>D. cd-databases provide a i>flexible framework for declaratively specifying the semantics of dd-databases: we can fix a standard i>control strategy, e.g., stable model or well-founded semantics, and vary the i>logical description i>Dcd for specifying different semantics. The i>transformed database i>Dcd usually consists of a part i>D⊗ which naturally expresses the rules of i>D, and two generic parts which are independent of i>D: i>Dlogic specifies i>logical inference rules like resolution and subsumption, and i>Dcwa specifies non-monotonic inference rules like i>closed-world-assumptions. Another i>program transformation, which uses the idea of bringing sets of clauses to the argument level is given for i>hypothetical logic programs: a hypothetical logic program i>D is mapped to a classical normal logic program i>Do, such that well-known semantics and inference methods for normal logic programs can be used for hypothetical reasoning as well.