Classical Modal De Morgan Algebras

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.