Power index-based semantics for ranking arguments in abstract argumentation frameworks

Ranking-based semantics for Abstract Argumentation Frameworks represent a well-established concept used for sorting a group of arguments from the most to the least acceptable. This paper describes a ranking-based semantics that makes use of power indexes such as the Shapley Value and the Banzhaf Power Index. This power index-based semantics is parametric to a chosen Dung semantics and inherits the properties of the index that is used for evaluating the arguments. We highlight the characteristics of the rankings obtained through different evaluation functions and we verify which of the properties from the literature are satisfied. Finally, we study the relation between the (skeptical/credulous) acceptability of an argument and its position in the ranking, thus designing new properties.