Stable Classes and Operator Pairs for Disjunctive Programs

. Baral and Subrahmanian introduced the notion of stable classes for normal logic programs. In contrast to stable models stable classes always exist and can be given a constructive characterization. We generalize the Baral-Subrahmanian approach to disjunctive programs and propose mf -stable classes for different functions mf . Such mf -stable classes always exist and are sound with respect to stable model semantics. Operationalizations for approximate but efficient query evaluation are defined in terms of three-valued interpretations and their relation with mf -stable classes is analyzed. Finally, analogous concepts are given for an approach based on states instead of models. 1 Introduction Stable model semantics as proposed by Gelfond and Lifschitz [5] is one of the most elegant approaches concerning the semantics of normal logic programs. It generalizes the perfect model semantics and is closely related with Autoepistemic Logic [14] as a major formalization of nonmonotonic reasoning..