Generalizing Complete Semantics to Bipolar Argumentation Frameworks

Computational models of argumentation are an interesting tool to represent decision processes. Bipolar abstract argumentation studies the question of which arguments a rational agent can accept given attack and support relationships between them. We present a generalization of the fundamental complete semantics from attack-only graphs to bipolar graphs. As opposed to previous semantics, the new bi-complete semantics treats attacks and supports symmetrically and directly leads to natural generalizations of grounded, preferred, semi-stable and stable semantics. We show, in particular, that bipolar graphs are strictly more expressive than attack-only graphs under bi-complete semantics. That is, the meaning of support edges cannot be encoded by attack edges like in deductive support frameworks.