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Polarity Semantics for Negation as a Modal Operator

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Abstract

The minimal weakening \({{\textsf {N}}}_0\) of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \({{\textsf {N}}}_0\) with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \({{\textsf {N}}}_0\). These logics have the finite model property and they are decidable.

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Acknowledgements

We give our thanks to the referees of the manuscript of this paper for their helpful comments. The authors were supported by Chinese National Foundation of Social Sciences (Grant No. 18ZDA033).

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

    Yuanlei Lin & Minghui Ma

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

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Lin, Y., Ma, M. Polarity Semantics for Negation as a Modal Operator. Stud Logica 108, 877–902 (2020). https://doi.org/10.1007/s11225-019-09879-w

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