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

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 th...

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Bibliographic Details
Published in:Theory and practice of logic programming Vol. 13; no. 1; pp. 107 - 142
Main Author: MAIER, FREDERICK
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.01.2013
Subjects:
Ambiguity
Constrictions
Formalism
Logic
Logic programming
Operators
Regular Papers
Semantics
Translations
well-founded semantics
logic programming
ambiguity blocking and propagation
defeasible logic
stable model semantics
ISSN:1471-0684, 1475-3081
Online Access:Get full text
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Summary: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.
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ISSN:1471-0684
1475-3081
DOI:10.1017/S147106841100041X