On Decision Problems Related to the Preferred Semantics for Argumentation Frameworks

Abstract

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.