Defense semantics of argumentation: revisit

Abstract: In this paper we introduce a novel semantics, called defense semantics, for Dung's abstract argumentation frameworks in terms of a notion of (partial) defence, which is a triple encoding that one argument is (partially) defended by another argument via attacking the attacker of the first argument. In terms of defense semantics, we show that defenses related to self-attacked arguments and arguments in 3-cycles are unsatifiable under any situation and therefore can be removed without affecting the defense semantics of an AF. Then, we introduce a new notion of defense equivalence of AFs, and compare defense equivalence with standard equivalence and strong equivalence, respectively. Finally, by exploiting defense semantics, we define two kinds of reasons for accepting arguments, i.e., direct reasons and root reasons, and a notion of root equivalence of AFs that can be used in argumentation summarization.