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Preferred extensions as stable models*

Published online by Cambridge University Press:  08 May 2008

JUAN CARLOS NIEVES ,
ULISES CORTÉS  and
MAURICIO OSORIO
JUAN CARLOS NIEVES
Affiliation:
Universitat Politècnica de Catalunya, Software Department (LSI), c/Jordi Girona 1-3, E08034, Barcelona, Spain (e-mail: jcnieves@lsi.upc.edu, ia@lsi.upc.edu)
ULISES CORTÉS
Affiliation:
Universitat Politècnica de Catalunya, Software Department (LSI), c/Jordi Girona 1-3, E08034, Barcelona, Spain (e-mail: jcnieves@lsi.upc.edu, ia@lsi.upc.edu)
MAURICIO OSORIO
Affiliation:
Universidad de las Américas – Puebla, CENTIA, Sta. Catarina Mártir, Cholula, Puebla, 72820México (e-mail: osoriomauri@googlemail.com)
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Abstract

Given an argumentation framework AF, we introduce a mapping function that constructs a disjunctive logic program P, such that the preferred extensions of AF correspond to the stable models of P, after intersecting each stable model with the relevant atoms. The given mapping function is of polynomial size w.r.t. AF.

In particular, we identify that there is a direct relationship between the minimal models of a propositional formula and the preferred extensions of an argumentation framework by working on representing the defeated arguments. Then we show how to infer the preferred extensions of an argumentation framework by using UNSAT algorithms and disjunctive stable model solvers. The relevance of this result is that we define a direct relationship between one of the most satisfactory argumentation semantics and one of the most successful approach of nonmonotonic reasoning i.e., logic programming with the stable model semantics.

Keywords

preferred semanticsabstract argumentation semanticsstable model semanticsminimal models
Type
Technical Note
Information
Theory and Practice of Logic Programming , Volume 8 , Issue 4 , July 2008 , pp. 527 - 543
Copyright
Copyright © Cambridge University Press 2008

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