Nested Sequents for Intuitionistic Modal Logics

We present cut-free deductive systems without labels for the intuitionistic variants of the modal logics obtained by extending K with a subset of the axioms d, t, b, 4, and 5. For this, we use the formalism of nested sequents. We show a uniform cut elimination argument and a terminating proof search procedure. As a corollary we get the decidability of all modal logics in the intuitionistic S5-cube. For most of the logics this has already been shown by other means, but for some cases, like intuitionistic S4, this solves an open problem.

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