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Falsification-Aware Calculi and Semantics for Normal Modal Logics Including S4 and S5

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Abstract

Falsification-aware (hyper)sequent calculi and Kripke semantics for normal modal logics including S4 and S5 are introduced and investigated in this study. These calculi and semantics are constructed based on the idea of a falsification-aware framework for Nelson’s constructive three-valued logic. The cut-elimination and completeness theorems for the proposed calculi and semantics are proved.

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Acknowledgements

We would like to thank the anonymous referee for his or her valuable comments and suggestions. This research was supported by JSPS KAKENHI Grant Numbers JP18K11171 and JP16KK0007 and Grant-in-Aid for Takahashi Industrial and Economic Research Foundation.

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  1. Department of Information and Electronic Engineering, Teikyo University, Toyosatodai 1-1, Utsunomiya, Tochigi, 320-8551, Japan

    Norihiro Kamide

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Kamide, N. Falsification-Aware Calculi and Semantics for Normal Modal Logics Including S4 and S5. J of Log Lang and Inf 32, 395–440 (2023). https://doi.org/10.1007/s10849-022-09386-7

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