Section: New Results

Nested Sequents for Intuitionistic Modal Logics

Participant : Lutz Straßburger.

We show how the recent results for treating classical modal logics in the modal cube under S5 via nested sequents  [32] , [33] can be carried to intuitionistic modal logics. Thus, we present cut-free nested sequent systems for all intuitionistic modal logics in the modal cube up to IS5, and we show how this can be done in a modular way, i.e., to each of the axioms d, t, b, 4, and 5, we assign a set of inference rules, such that for each subset of d,t,b,4,5 the corresponding set of rules is sound and complete for the defined logic. This work has been presented in an invited talk at the IMLA workshop in Nancy [25] .