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BK-lattices. Algebraic Semantics for Belnapian Modal Logics

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Abstract

Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK-lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK-lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK. Finally, we describe invariants determining a twist-structure over a modal algebra.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Koptyug prosp. 4, 630090, Novosibirsk, Russia

    Sergei P. Odintsov

  2. Novosibirsk State University, Pirogova 2, 630090, Novosibirsk, Russia

    Sergei P. Odintsov & E. I. Latkin

Authors
  1. Sergei P. Odintsov
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  2. E. I. Latkin
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Correspondence to Sergei P. Odintsov.

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In memoriam Leo Esakia

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Odintsov, S.P., Latkin, E.I. BK-lattices. Algebraic Semantics for Belnapian Modal Logics. Stud Logica 100, 319–338 (2012). https://doi.org/10.1007/s11225-012-9380-4

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  • DOI: https://doi.org/10.1007/s11225-012-9380-4

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