Classical Modal De Morgan Algebras

Studia Logica 98 (1-2):251-266 (2011)
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
Keywords modal operator  De Morgan algebras  Amalgamation property
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DOI 10.1007/s11225-011-9328-0
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Isabel Loureiro (1983). Prime Spectrum of a Tetravalent Modal Algebra. Notre Dame Journal of Formal Logic 24 (3):389-394.

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