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Embedding defeasible logic into logic programming

Published online by Cambridge University Press:  16 October 2006

GRIGORIS ANTONIOU
Affiliation:
Institute of Computer Science, FORTH, Greece (e-mail: antoniou@ics.forth.gr)
DAVID BILLINGTON
Affiliation:
School of ICT, Griffith University, Australia (e-mail: d.billington@griffith.edu.au)
GUIDO GOVERNATORI
Affiliation:
School of ITEE, University of Queensland, Australia (e-mail: guido@itee.uq.edu.au)
MICHAEL J. MAHER
Affiliation:
National ICT Australia, c/o UNSW, Australia (e-mail: mmaher@cse.unsw.edu.au)

Abstract

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory $D$ into a meta-program $P(D)$. We show that under a condition of decisiveness, the defeasible consequences of $D$ correspond exactly to the sceptical conclusions of $P(D)$ under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of $D$ are included in all stable models of $P(D)$). If we wish a complete embedding for the general case, we need to use the Kunen semantics of $P(D)$, instead.

Type
Regular Papers
Copyright
2006 Cambridge University Press

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