Categorical study for algebras of Fitting's lattice-valued logic and lattice-valued modal logic

The paper explores categorical interconnections between lattice-valued relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued Boolean systems, and then we study adjointness and co-adjointness of functors defined on them. As a result, we get a duality f...

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Bibliographic Details
Published inAnnals of mathematics and artificial intelligence Vol. 89; no. 3-4; p. 409
Main Authors Ray, Kumar Sankar, Das, Litan Kumar
Format Journal Article
LanguageEnglish
Published Springer 01.03.2021
Subjects
Algebra
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Summary:The paper explores categorical interconnections between lattice-valued relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued Boolean systems, and then we study adjointness and co-adjointness of functors defined on them. As a result, we get a duality for algebras of lattice-valued logic. Following this duality result, we establish a duality for algebras of lattice-valued modal logic. Keywords Lattice-valued Boolean systems * Lattice-valued relational systems * Algebras of Fitting's lattice-valued modal logic * Adjoint * Co-adjoint * Duality Mathematics Subject Classification (2010) 03B50 * 06D22 * 06D50 * 18B99
ISSN:1012-2443
DOI:10.1007/[s.sub.1]0472-020-09707-1