Disjunctive Logic Programs with Negation

Recently the study of theoretical foundations of disjunctive logic programs with default negation has attracted considerable attention. This is mainly because the additional expressive power of disjunctive logic programs significantly simplifies the problem of modeling disjunctive statements of various nonmonotonic formalisms in the framework of logic programming, and consequently facilitates the use of logic programming as an inference engine for nonmonotonic reasoning.

Our general goal here is to use Kripke structures of autoepistemic logic as a tool to classify disjunctive program semantics. Logics of knowledge and belief provide a theoretical foundation for logic programming semantics while Kripke structures capture model semantics of the logic. However, logic programming semantics have rarely been characterized in terms of Kripke structures, which is quite unusual. The main reason, we believe, is that the Kripke structure, as with any other model theoretical tools, is an ideal tool for capturing monotonic semantics of logic of knowledge and belief but it has inherent difficulty in characterizing negative introspection, which forms the basis for default reasoning. Thus, the focus of this research project is how to characterize negative introspection in terms of accessibility relations of Kripke structures.

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