Ranking-Based Semantics for Sets of Attacking Arguments

Argumentation is a process of evaluating and comparing sets of arguments. Ranking-based semantics received a lot of attention recently. All of the semantics introduced so far are applicable to binary attack relations. In this paper, we study a more general case when sets of arguments can jointly attack an argument. We generalise existing postulates for ranking-based semantics to fit this framework, define a general variant of h-categoriser, prove that it converges for every argumentation framework and study the postulates it satisfies. We also study the link between binary and hypergraph version of h-categoriser.