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Refutation-Aware Gentzen-Style Calculi for Propositional Until-Free Linear-Time Temporal Logic

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Abstract

This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style semantics for propositional until-free linear-time temporal logic. The sequent calculi and semantics are constructed on the basis of the refutation-aware setting for Nelson’s paraconsistent logic. The cut-elimination and completeness theorems for the proposed sequent calculi and semantics are proven.

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Acknowledgements

We would like to thank the anonymous referees for their valuable comments and suggestions. This research was supported by JSPS KAKENHI Grant Number JP23K10990.

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  1. Department of Data Science, School of Data Science, Nagoya City University, Takiko Campus, Yamanohata 1, Mizuho-cho, Mizuho-ku, Nagoya, Aichi, 467-8501, Japan

    Norihiro Kamide

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Kamide, N. Refutation-Aware Gentzen-Style Calculi for Propositional Until-Free Linear-Time Temporal Logic. Stud Logica 111, 979–1014 (2023). https://doi.org/10.1007/s11225-023-10052-7

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