Using clausal deductive databases for defining semantics in disjunctive deductive databases

Abstract

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