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Belnap–Dunn Modal Logic with Value Operators

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Abstract

The language of Belnap–Dunn modal logic \({\mathscr {L}}_0\) expands the language of Belnap–Dunn four-valued logic (having constant symbols for the values 0 and 1) with the modal operator \(\Box \). We introduce the polarity semantics for \({\mathscr {L}}_0\) and its two expansions \({\mathscr {L}}_1\) and \({\mathscr {L}}_2\) with value operators. The local finitary consequence relation \(\models _4^k\) in the language \({\mathscr {L}}_k\) with respect to the class of all frames is axiomatized by a sequent system \(\mathsf {S}_k\) where \(k=0, 1, 2\). We prove by using translations between sequents and formulas that these languages under the polarity semantics have the same expressive power on the level of frames with the language \({\mathscr {L}}_0\) under the relational semantics for classical modal logic.

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Change history

  • 02 July 2021

    The DOI URL in the reference [24] was incorrectly published. It has been corrected from https://doi.org/10.1017/s17550203119000121 to https://doi.org/10.1017S1755020319000121.

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Acknowledgements

The fund was provide by Chinese National Funding of Social Sciences (Grant No. 18ZDA033).

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Authors and Affiliations

  1. Department of Philosophy, Nanchang University, Xuefu Road 999, Honggutan District, Nanchang, China

    Yuanlei Lin

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

    Minghui Ma

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  1. Yuanlei Lin
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Correspondence to Minghui Ma.

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Lin, Y., Ma, M. Belnap–Dunn Modal Logic with Value Operators. Stud Logica 109, 759–789 (2021). https://doi.org/10.1007/s11225-020-09925-y

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