Stable and Extension Class Theory for
Logic Programs and Default Logics
Chitta R. Baral and V.S. Subrahmanian
Abstract
The stable model semantics (cf. Gelfond and
Lifshitz \cite{Gelf88}) 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 \cite{Mare88a} relating
logic programming and default logics.