Characterizations of Stable Model Semantics for Logic Programs with Arbitrary Constraint Atoms

TL;DR

This paper introduces a compact representation of constraint atoms in logic programs, generalizes stable model semantics to include disjunctive and arbitrary constraint atoms, and extends dependency analysis techniques.

Contribution

It provides a unified framework for stable model semantics with constraint atoms, enabling applications to disjunctive programs and dependency characterizations.

Findings

Generalizes Gelfond-Lifschitz transformation for constraint atoms

Defines stable models for disjunctive logic programs with constraints

Extends dependency analysis to programs with constraint atoms

Abstract

This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond-Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al., which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.