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

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Abstract

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.

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Authors and Affiliations

  1. ECSU, Indian Statistical Institute, Kolkata, India

    Kumar Sankar Ray & Litan Kumar Das

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  1. Kumar Sankar Ray
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  2. Litan Kumar Das
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Correspondence to Kumar Sankar Ray.

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Ray, K.S., Das, L.K. Categorical study for algebras of Fitting’s lattice-valued logic and lattice-valued modal logic. Ann Math Artif Intell 89, 409–429 (2021). https://doi.org/10.1007/s10472-020-09707-1

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  • DOI: https://doi.org/10.1007/s10472-020-09707-1

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Mathematics Subject Classification (2010)