Abstract
This paper provides a method to obtain terminating analytic calculi for a large class of intuitionistic modal logics. For a given logic L with a cut-free calculus G that is an extension of G3ip the method produces a terminating analytic calculus that is an extension of G4ip and equivalent to G. G4ip was introduced by Roy Dyckhoff in 1992 as a terminating analogue of the calculus G3ip for intuitionistic propositional logic. Thus this paper can be viewed as an extension of Dyckhoff’s work to intuitionistic modal logic.
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Acknowledgements
I thank Iris van der Giessen for the pleasant collaboration that lead to two papers [8, 9] that were the inspiration for the material presented in this paper. I thank an anonymous referee for the useful remarks on an earlier draft of this paper. Support by the Netherlands Organisation for Scientific Research under grant 639.073.807 is gratefully acknowledged.
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Iemhoff, R. The G4i Analogue of a G3i Sequent Calculus. Stud Logica 110, 1493–1506 (2022). https://doi.org/10.1007/s11225-022-10008-3
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DOI: https://doi.org/10.1007/s11225-022-10008-3