An Extension-Based Argument-Ranking Semantics: Social Rankings in Abstract Argumentation

In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social ranking functions which have been developed recently to rank individuals based on their performance in groups. We provide necessary and sufficient conditions for a social ranking function to give rise to an argument-ranking semantics satisfying the desired refinement property. Moreover, we analyse the properties of the argument-ranking semantics induced by the most prominent social ranking function that satisfies all of these conditions by investigating the satisfaction of principles known from the argument-ranking literature.