From Individual to Collective Argumentation: Aggregating Acyclic Argumentation Frameworks

Abstract

An argumentation framework consists of a class of arguments and an abstract attack relation among them. The same arguments, but under different attack relationships, yield different frameworks. We analyze here how to merge frameworks with a common set of arguments; we proceed by aggregating the attack relations. A positive result ensues for certain classes of attack relations. In particular, in the case of acyclic attack relations, where the aggregation is obtained under the same conditions as Arrow’s Theorem. These conditions involve certain properties of fairness of the aggregation process. The acyclicity of the attack relations implies that, if the class of winning coalitions in the voting-based aggregation process is a proper prefilter, a single attack relation can be obtained. While many properties of the individual frameworks are preserved in the consequent merged framework, this procedure does not yield the same results when the aggregation is applied on the extensions of argumentation frameworks.