Hypersequent-Based Argumentation: An Instantiation in the Relevance Logic RM

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 us to overcome some of the weaknesses of logical argumentation reported in the literature and to prove several desirable properties, stated in terms of rationality postulates. For this, we take the relevance logic RM as the deductive base of our formalism. This logic is regarded as “by far the best understood of the Anderson-Belnap style systems” (Dunn and Restall, Handbook of Philosophical Logic, vol. 6). It has a clear semantics in terms of Sugihara matrices, as well as sound and complete Hilbert- and Gentzen-type proof systems. The latter are defined by hypersequents and admit cut elimination. We show that hypersequent-based argumentation yields a robust defeasible variant of RM with many desirable properties (e.g., rationality postulates and crash-resistance).