Encompassing Attacks to Attacks in Abstract Argumentation Frameworks

Abstract

In the traditional definition of Dung's abstract argumentation framework ($\ensuremath{AF}$), the notion of attack is understood as a relation between arguments, thus bounding attacks to start from and be directed to arguments. This paper introduces a generalized definition of abstract argumentation framework called $\ensuremath{AFRA}$ (Argumentation Framework with Recursive Attacks), where an attack is allowed to be directed towards another attack. From a conceptual point of view, we claim that this generalization supports a straightforward representation of reasoning situations which are not easily accommodated within the traditional framework. From the technical side, we first investigate the extension to the generalized framework of the basic notions of conflict-free set, acceptable argument, admissible set and of Dung's fundamental lemma. Then we propose a correspondence from the $\ensuremath{AFRA}$ to the $\ensuremath{AF}$ formalism, showing that it satisfies some basic desirable properties. Finally we analyze the relationships between $\ensuremath{AFRA}$ and a similar extension of Dung's abstract argumentation framework, called $\ensuremath{EAF+}$ and derived from the recently proposed formalism $\ensuremath{EAF}$.