The Alternating Semantics for Default Theories and Logic Programs

In this paper we propose a semantics for default theories, based on van Gelder's alternating fixpoint theory. The distinct feature of this semantics is its preservation of Reiter's semantics when a default theory is not considered "problematic" under Reiter's semantics. Differences arise only when a default theory has no extensions, or has only "biased extensions" under Reiter's semantics. This feature allows skeptical reasoning in Reiter's logic to be properly preserved in the new semantics. By the familiar, natural translation from logic programs to default theories, the semantics proposed for default theories provides a natural extension to the stable model semantics of normal logic programs. 1 Introduction Default logic, introduced by Reiter [7], forms one of the most important formalisms for nonmonotonic reasoning. One of the problems with this default logic is that a reasonable default theory may not always have extensions. In such a case, the semantics of the default theory is ..