Theory and Practice of Logic Programming

Table of Contents - 2008 - Volume 8, Issue 04  

Technical Note

Preferred extensions as stable models*

JUAN CARLOS NIEVESa1, ULISES CORTÉSa1 and MAURICIO OSORIOa2

a1 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)

a2 Universidad de las Américas – Puebla, CENTIA, Sta. Catarina Mártir, Cholula, Puebla, 72820 México (e-mail: osoriomauri@googlemail.com)

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.

(Received June 06 2007)

(Revised December 17 2007)

(Accepted February 29 2008)

KEYWORDS:

  • preferred semantics;
  • abstract argumentation semantics;
  • stable model semantics;
  • minimal models

Footnotes

* This is a revised and improved version of the paper Inferring preferred extensions by minimal models which appeared in Guillermo R. Simari and Paolo Torroni (Eds), proceedings of the workshop Argumentation and Non-Monotonic Reasoning (LPNMR-07 Workshop).