The Alternating Semantics for Default Theories and Logic Programs

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  • Technical report TR92-16. Recent proposals for semantics of default theories are all based on some types of weaker notion of extensions. This is typified in the well-founded semantics and the extension class semantics for default theories. Although these semantics solve the no-extension problem in Reiter's default logic, they also present a departure from Reiter's original extension semantics, even for default theories which can be completely characterized by the extension semantics. This results in a weaker capability for skeptical reasoning. 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. | TRID-ID TR92-16

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    Attribution 3.0 International