Towards a general model for abstract argumentation frameworks

In its original definition, the Abstract Argumentation framework considers atomic claims and a binary attack relationship among them, based on which different semantics would select subsets of claims consistently supporting the same position in a dispute or debate. While attack is obviously the core relationship in this setting, in more complex (and in many real-world) situations additional information may help, or might even be crucial, in determining such positions, and especially those that are going to win the debate. Examples are bipolarity (considering also the support relationship between pairs of claims) and weights (assigning different importance to different elements of the framework). These additional features have often been considered separately, yielding incompatible or anyhow disjoint models for argumentation frameworks. In this paper we propose a model that unifies all these perspectives, and further extends them by allowing to express contextual information associated to the arguments, in addition to their relationships.