Dialectic semantics for argumentation frameworks

Abstract

We provide a formalism for the study of dialogues, where a dialogue is a two-person game, initiated by the proponent who defends a proposed thesis. We examine several different winning criteria and several different dialogue types, where a dialogue type is determined by a set of positions, an attack relation between positions and a legal-move function. We examine two proof theories, where a proof theory is determined by a dialogue type and a winning criterion. For each of the proof theories we supply a corresponding declarative semantics.