On the Acceptability of Incompatible Arguments

In this paper we study the acceptability of incompatible arguments within Dung’s abstract argumentation framework. As an example we introduce an instance of Dung’s framework where arguments are represented by propositional formulas and an argument attacks another one when the conjunction of their representations is inconsistent, which we characterize as a kind of symmetric attack. Since symmetric attack is known to have the drawback to collapse the various argumentation semantics, we consider also two variations. First, we consider propositional arguments distinguishing support and conclusion. Second, we introduce a preference ordering over the arguments and we define the attack relation in terms of a symmetric incompatibility relation and the preference relation. We show how to characterize preference-based argumentation using a kind of acyclic attack relation.