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Stable classes and operator pairs for disjunctive programs
Stable Classes and Operator Pairsfor Disjunctive ProgramsJurgen KalinskiInstitute of Computer Science IIIUniversity of Bonn, Romerstr.Bonn, Germanyemail: cully@cs.uni-bonn.deAbstract. Baral and Subrahmanian introduced the notion of stableclasses for normal logic programs. In contrast to stable models stableclasses always exist and can be given a constructive characterization.We generalize the Baral-Subrahmanian approach to disjunctive programsand propose mf -stable classes for di erent functions mf . Such mf -stableclasses always exist and are sound with respect to stable model seman-tics. Operationalizations for approximate but ecient query evaluationare de ned in terms of three-valued interpretations and their relationwith mf -stable classes is analyzed. Finally, analogous concepts are givenfor an approach based on states instead of models.1 IntroductionStable model semantics as proposed by Gelfond and Lifschitz [5] is one of themost elegant approaches concerning the semantics of normal logic programs. Itgeneralizes the perfect model semantics and is closely related with Autoepis-temic Logic [14] as a major formalization of nonmonotonic reasoning. Further-more, stable model semantics could subsequently be extended to disjunctive logicprograms (Gelfond and Lifschitz [6], by Przymusinski [17]).Unfortunately, stable models do not necessarily exist, and even when theyexist they are hard to compute. Baral and Subrahmanian therefore introducedthe notion of stable classes for normal programs (cf. [2] and [3]). Essentially, astable class is a set I of interpretations such thatI = fSP (I) j I 2 I gwhere SP is an antimonotonic operator. They prove that normal programs alwayshave stable classes and thatf lfp (S2P ); gfp (S2P ) gis the smallest (with respect to a Hoare-ordering) stable class, thereby providinga constructive characterization. They furthermore show that this stable class isequivalent to the well-founded semantics, another (by now) standard formaliz
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