A default approach to semantics of logic programs with constraint atoms

Abstract

We define the semantics of logic programs with (abstract) constraint atoms in a way closely tied to default logic. Like default logic, formulas in rules are evaluated using the classical entailment relation, so a constraint atom can be represented by an equivalent propositional formula. Therefore, answer sets are defined in a way closely related to default extensions. The semantics defined this way enjoys two properties generally considered desirable for answer set programming - minimality and derivability. The derivability property is very important because it guarantees free of self-supporting loops in answer sets. We show that when restricted to basic logic programs, this semantics agrees with the conditional-satisfaction based semantics. Furthermore, answer sets by the minimal-model based semantics can be recast in our approach. Consequently, the default approach gives a unifying account of the major existing semantics for logic programs with constraint atoms. This also makes it possible to characterize, in terms of the minimality and derivability properties, the precise relationship between them and contrast with others. © 2009 Springer Berlin Heidelberg.