Stable theories for logic programs

Abstract

We define a class of theories associated to any normal logic program, called stable theories, based on a notion of stable negative hypotheses. This stability of hypotheses is motivated directly from the intuitive understanding of negation by failure. We study how stable theories generalize stable models and show that every logic program has at least one stable theory associated to it. Also the same basic ideas allow us to identify a unique theory that defines a ``minimal'' semantics for logic programs analogous to the well-founded model semantics. This provides a uniform framework that accommodates these two different semantics of stable and well-founded model and clarifies further their relationship.