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Neighbourhood Semantics for FDE-Based Modal Logics

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Abstract

We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap’s and M. Dunn’s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of \(\mathsf {BK}\), \(\mathsf {BK^{FS}}\) and \(\mathsf {MBL}\).

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Acknowledgements

The work reported in this paper has been carried out as part of the research project “FDE-based Modal Logics”, supported by the Deutsche Forschungsgemeinschaft, DFG, grant WA 936/13-1, and the Russian Foundation for Basic Research, RFBR, grant No. 18-501-12019. We gratefully acknowledge this support. We also thank an anonymous reviewer for some useful comments which helped improve the presentation of the paper.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk, Russian Federation, 630090

    S. Drobyshevich

  2. Novosibirsk State University, 2 Pirogova Street, Novosibirsk, Russian Federation, 630090

    S. Drobyshevich

  3. Department of Philosophy I, Ruhr University Bochum, Universitätsstraße 150, 44801, Bochum, Germany

    D. Skurt

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  1. S. Drobyshevich
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  2. D. Skurt
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Correspondence to S. Drobyshevich.

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Drobyshevich, S., Skurt, D. Neighbourhood Semantics for FDE-Based Modal Logics. Stud Logica 109, 1273–1309 (2021). https://doi.org/10.1007/s11225-021-09948-z

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