Hypersequential Argumentation Frameworks: An Instantiation in the Modal Logic S5

In this paper we introduce hypersequent-based frameworks for the modeling of defeasible reasoning by means of logic-based argumentation. These frameworks are an extension of sequent-based argumentation frameworks, in which arguments are represented not only by sequents, but by more general expressions, called hypersequents. This generalization allows to incorporate, as the deductive base of our formalism, some well-studied logics like the modal logic S5, the relevant logic RM, and Godel-Dummett logic LC, to which no cut-free sequent calculi are known. In this paper we take S5 as the core logic and show that the hypersequent-based argumentation frameworks that are obtained in this case yield a robust defeasible variant of S5 with several desirable properties.