Reducts of propositional theories, satisfiability relations, and generalizations of semantics of logic programs

Abstract

Over the years, the stable-model semantics has gained a position of the correct (two-valued) interpretation of default negation in programs. However, for programs with aggregates (constraints), the stable-model semantics, in its broadly accepted generalization stemming from the work by Pearce, Ferraris and Lifschitz, has a competitor: the semantics proposed by Faber, Leone and Pfeifer, which seems to be essentially different. Our goal is to explain the relationship between the two semantics. Pearce, Ferraris and Lifschitz's extension of the stable-model semantics is best viewed in the setting of arbitrary propositional theories. We propose an extension of the Faber-Leone-Pfeifer semantics, or FLP semantics, for short, to the full propositional language, which reveals both common threads and differences between the FLP and stable-model semantics. We establish several properties of the FLP semantics. We apply a similar approach to define supported models for arbitrary propositional theories. © 2009 Springer Berlin Heidelberg.