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Interdefinability of defeasible logic and logic programming under the well-founded semantics

Published online by Cambridge University Press:  09 August 2011

FREDERICK MAIER
FREDERICK MAIER*
Affiliation:
Kno.e.sis Center, Department of Computer Science & Engineering, Wright State University, 3640 Colonel Glenn Hwy, Dayton, OH 45435, USA (e-mail: [email protected], [email protected])
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Abstract

We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond–Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.

Keywords

defeasible logiclogic programmingwell-founded semanticsstable model semanticsambiguity blocking and propagation
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 13 , Issue 1 , January 2013 , pp. 107 - 142
Copyright
Copyright © Cambridge University Press 2011

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