We give a procedure for translating geometric Kripke frame axioms into structural hypersequent rules for the corresponding intermediate logics in Int/Geo that admit weakening, contraction and in some cases, cut. We give a procedure for translating labelled sequents in the corresponding logic to hypersequents that share the same linear models (which correspond to Gödel-Dummett logic). We prove t...

Since the ground-breaking contributions of M. Dummett (Dummett 1978), it is widely recognized that anti-realist principles have a critical impact on the choice of logic. Dummett argued that classical logic does not satisfy the requirements of such principles but that intuitionistic logic does. Some philosophers have adopted a more radical stance and argued for a more important departure from cl...

It is well-known that weakening and contraction cause näıve categorical models of the classical sequent calculus to collapse to Boolean lattices. In previous work, summarized briefly herein, we have provided a class of models called classical categories which is sound and complete and avoids this collapse by interpreting cut-reduction by a poset-enrichment. Examples of classical categories incl...

Building on a version of Lorenzen’s dialogue foundation for intuitionistic logic, we show that Gödel-Dummett logic G can be characterized by a suitable game of communicating parallel dialogues. This provides a computational interpretation of Avron’s hypersequent calculus for G.

This paper discusses a new strategy to decide Dummett logic. The strategy relies on a tableau calculus whose distinguishing features are the rules for implicative formulas. The strategy has been implemented and the experimental results are reported.

We present a procedure to decide propositional Dummett logic. This procedure relies on a tableau calculus with a multiple premise rule and optimizations. The resulting implementation outperforms the state of the art graph-based procedure.