Cut elimination in nested sequents for intuitionistic modal logics

Authors:
Lutz Straßburger
Affiliations:
INRIA Saclay---Île-de-France -- Équipe-projet Parsifal, École Polytechnique -- LIX, Palaiseau Cedex, France
Venue:
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
Year:
2013

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Abstract

We present cut-free deductive systems without labels for the intuitionistic variants of the modal logics obtained by extending IK with a subset of the axioms d, t, b, 4, and 5. For this, we use the formalism of nested sequents, which allows us to give a uniform cut elimination argument for all 15 logic in the intuitionistic S5 cube.