Dialectical Proof Theories for the Credulous Prudent Preferred Semantics of Argumentation

In Dung’s argumentation system, acceptable sets of arguments are defined as sets of arguments that attack all their attackers, and that do not contain any direct contradiction. However, in many applications, the presence of indirect contradictions should prevent a set from being acceptable. The family of prudent semantics has been proposed as an answer to this problem. We are interested in this paper in determining whether a given set of arguments is included in at least one acceptable set under the prudent preferred semantics. To this end, we propose a dialectical framework and several proof theories.