Stable models and non-determinism in logic programs with negation

Abstract

Previous researchers have proposed generalizations of Horn clause logic to support negation and non-determinism as two separate extensions. In this paper, we show that the stable model semantics for logic programs provides a unified basis for the treatment of both concepts. First, we introduce the concepts of partial models, stable models, strongly founded models and deterministic models and other interesting classes of partial models and study their relationships. We show that the maximal deterministic model of a program is a subset of the intersection of all its stable models and that the well-founded model of a program is a subset of its maximal deterministic model. Then, we show that the use of stable models subsumes the use of the non-deterministic choice construct in LDL and provides an alternative definition of the semantics of this construct. Finally, we provide a constructive definition for stable models with the introduction of a procedure, called backtracking fixpoint, that non-deterministically constructs a total stable model, if such a model exists.