Alternating fixpoint theory for logic programs with priority

Abstract

van Gelder's alternating fixpoint theory has proven to be a very useful tool for unifying and characterizing various semantics for logic programs without priority. In this paper we propose an extension of van Gelder's alternating fixpoint theory and show that it can be used as a general semantic framework for logic programs with priority. Specifically, we define three declarative and model-theoretic semantics in this framework for prioritied logic programs: prioritized answer sets, prioritized regular extensions and prioritized well-founded model. We show that all of these semantics are natural generalizations of the corresponding semantics for logic programs without priority. We also show that these semantics have some other desirable properties. In particular, they can handle conflicts caused indirectly by the priorities.