On the equivalence of the static and disjunctive well-founded semantics and its computation

Abstract

In recent years, much work was devoted to the study of theoretical foundations of Disjunctive Logic Programming and Disjunctive Deductive Databases. While the semantics of non-disjunctive programs is fairly well understood, the declarative and computational foundations of disjunctive logic programming proved to be much more elusive and difficult. Recently, two new and promising semantics have been proposed for the class of disjunctive logic programs. The first one is the static semantics STATIC, proposed by Przymusinski, and, the other is the disjunctive well-founded semantics D-WFS, proposed by Brass and Dix. Although the two semantics are based on very different ideas, both of them have been shown to share a number of natural and intuitive properties. In particular, both of them extend the well-founded semantics of normal logic programs. Nevertheless, since the static semantics employs a much richer underlying language than the D-WFS semantics, in general, the two semantics are different. The main result of this paper shows, however, that, when restricted to a common language, the two semantics in fact coincide. This important result provides additional and powerful argument in favor of the two semantics. It also allows us to use a recently developed minimal model theorem prover for an efficient implementation of the two semantics.