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Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic

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Abstract

Quasi-Boolean modal algebras are quasi-Boolean algebras with a modal operator satisfying the interaction axiom. Sequential quasi-Boolean modal logics and the relational semantics are introduced. Kripke-completeness for some quasi-Boolean modal logics is shown by the canonical model method. We show that every descriptive persistent quasi-Boolean modal logic is canonical. The finite model property of some quasi-Boolean modal logics is proved. A cut-free Gentzen sequent calculus for the minimal quasi-Boolean logic is developed and we show that it has the Craig interpolation property.

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Acknowledgements

Thanks are given to the referee’s for their helpful comments on revising the manuscript. The work of the authors was supported by Chinese National Funding of Social Sciences (18ZDA033).

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Authors and Affiliations

  1. Institute of Logic and Cognition Department of Philosophy, Sun Yat-sen University, Xingang Xi Road 135, Guangzhou, 510275, China

    Minghui Ma & Juntong Guo

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  1. Minghui Ma
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  2. Juntong Guo
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Correspondence to Minghui Ma.

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Ma, M., Guo, J. Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10095-4

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