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Classical Modal De Morgan Algebras

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Abstract

In this note we introduce the variety \({{\mathcal C}{\mathcal D}{\mathcal M}_\square}\) of classical modal De Morgan algebras as a generalization of the variety \({{{\mathcal T}{\mathcal M}{\mathcal A}}}\) of Tetravalent Modal algebras studied in [11]. We show that the variety \({{\mathcal V}_0}\) defined by H. P. Sankappanavar in [13], and the variety S of Involutive Stone algebras introduced by R. Cignoli and M. S de Gallego in [5], are examples of classical modal De Morgan algebras. We give a representation theory, and we study the regular filters, i.e., lattice filters closed under an implication operation. Finally we prove that the variety \({{{\mathcal T}{\mathcal M}{\mathcal A}}}\) has the Amalgamation Property and the Superamalgamation Property.

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  1. CONICET and Departamento de Matemáticas, Universidad Nacional del Centro, Pinto 699, Tandil, Argentina

    Sergio A. Celani

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  1. Sergio A. Celani
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Correspondence to Sergio A. Celani.

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Celani, S.A. Classical Modal De Morgan Algebras. Stud Logica 98, 251–266 (2011). https://doi.org/10.1007/s11225-011-9328-0

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