BK-lattices. Algebraic Semantics for Belnapian Modal Logics

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...

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Bibliographic Details
Published inStudia logica Vol. 100; no. 1/2; pp. 319 - 338
Main Authors Odintsov, S.P., Latkin, E.I.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer 01.04.2012
Springer Netherlands
Subjects
Abstract algebraic logic
Abstract logic
Algebra
Axioms
Boolean algebras
Computational Linguistics
Education
Equivalence relation
Logic
Logical theorems
Mathematical logic
Mathematical Logic and Foundations
Modal logic
Philosophy
Semantics
twist-structure
Belnapian modal logic
lattice
lattice of subvarieties
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Summary: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.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-012-9380-4