Stable and extension class theory for logic programs and default logics

The stable model semantics (cf. Gelfond and Lifschitz [1]) for logic programs suffers from the problem that programs may not always have stable models. Likewise, default theories suffer from the problem that they do not always have extensions. In such cases, both these formalisms for non-monotonic reasoning have an inadequate semantics. In this paper, we propose a novel idea-that of extension classes for default logics, and of stable classes for logic programs. It is shown that the extension class and stable class semantics extend the extension and stable model semantics respectively. This allows us to reason about inconsistent default theories, and about logic programs with inconsistent completions. Our work extends the results of Marek and Truszczynski [2] relating logic programming and default logics.