The Alternating Semantics for Default Theories and Logic Programs

Abstract

Recent proposals for semantics of default theories are all based on some types of weaker notion of extensions This is typi ed 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 char acterized 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 xpoint 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 Di erences 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 The paper has been printed as a Technical Report TR Department of Computing Science Uni versity of Alberta