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A Proof-Theoretic Approach to Negative Translations in Intuitionistic Tense Logics

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Abstract

A cut-free Gentzen sequent calculus for Ewald’s intuitionistic tense logic \(\mathsf {IK}_t\) is established. By the proof-theoretic method, we prove that, for every set of strictly positive implications S, the classical tense logic \({\mathsf {K}}_t\oplus S\) is embedded into its intuitionistic analogue \(\mathsf {IK}_t\oplus S\) via Kolmogorov, Gödel–Genzten and Kuroda translations respectively. A sufficient and necessary condition for Glivenko type theorem in tense logics is established.

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Acknowledgements

The work of the first author was supported by the Project of National Social Science Found of China (Grant No. 17CZX048). Thanks are given to the referee for helpful comments on the manuscript.

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Authors and Affiliations

  1. Department of Philosophy, Xiamen University, Siming Nan No. 422, Xiamen, China

    Zhe Lin

  2. Department of Philosophy, Institute of Logic and Cognition, Sun Yat-sen University, Xingangxi Road 135, Guangzhou, China

    Minghui Ma

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  1. Zhe Lin
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  2. Minghui Ma
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Correspondence to Minghui Ma.

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Lin, Z., Ma, M. A Proof-Theoretic Approach to Negative Translations in Intuitionistic Tense Logics. Stud Logica 110, 1255–1289 (2022). https://doi.org/10.1007/s11225-022-10003-8

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