Logical foundations for bipolar and tripolar argumentation networks: Preliminary results

Traditional abstract argumentation networks have been studied in two directions Investigate their semantics in detail. This has lead to the study of extensions, dealing with loops, connections with classical logic, the notions joint and disjunctive attacks, and especially what concerns us here, the Equational approach and the ASPIC instantiation approach. Generalize the notion of argumentation to bipolar argumentation and to the addition of the notion of support. This article will study bipolar and tripolar argumentation networks, both from the equational point of view and by reducing them to traditional attack network. The article will avoid traditional difficulties with bipolar networks and, most importantly, it will indicate how to model the ASPIC approach (see M. Caminada and L. Amgoud. On the evaluation of argumentation formalisms), using tripolar equational networks with joint support.