Extension-ranking Semantics for Abstract Argumentation

In this paper, we present a general framework for ranking sets of arguments in abstract argumentation frameworks based on their plausibility of acceptance. We present a generalisation of Dung’s extension semantics as extension-ranking semantics, which induce a preorder over the power set of all arguments, allowing us to state that one set is “closer” to being acceptable than another. To evaluate the extension-ranking semantics, we introduce a number of principles that a well-behaved extensionranking semantics should satisfy. We consider several simple base relations, each of which models a single central aspect of argumentative reasoning. The combination of these base relations provides us with a family of extension-ranking semantics.