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OUP > Journals > Computing/Engineer. & Mathematics/Stats. > Journal of Logic and Computation

Journal of Logic and Computation

Computational Dialectics

Volume 13, Issue 3, June 2003: pp. 377-403

Original Article
On Decision Problems Related to the Preferred Semantics for Argumentation Frameworks

Claudette Cayrol1, Sylvie Doutre1 and Jerome Mengin1

1IRIT, 118 route de Narbonne, 31062 Toulouse Cedex, France. E-mail: ccayrol@irit.fr, doutre@irit.fr, mengin@irit.fr

Argumentation is a form of reasoning, in which two agents cooperate in order to establish the validity of a given argument; this argument could be used to deduce some conclusion of interest. In this article, we look at the credulous and the sceptical decision problems under Dung's preferred semantics, that is, the problems of deciding if an argument belongs to one or to every preferred extension of an argumentation framework. We present two proof theories for the credulous decision problem and an algorithm which computes one of them. We show how these proof theories can be used for the sceptical decision problem in two particular cases of argumentation frameworks and we give an algorithm which answers that problem in the general case.

Keywords: Argumentation, decision problems, preferred semantics, proof theory.

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