Beyond admissibility: accepting cycles in argumentation with game protocols for cogency criteria

In this article, we extend Dung's formal approach from admissibility to less demanding extension semantics allowing arguments in cycles of attacks. We present an acceptance criterion leading to the characterization of three semantics called pairwise cogency , weak cogency and cyclic cogency . Particular game-theoretic protocols allow us to identify winning strategies with extensions in different semantics. Furthermore, an algorithmic characterization of those games exhibits clearly how self-attacking or in odd-length cycles of attack can be rationally managed beyond the limits of admissibility.