On PBZ*-lattices

Abstract

We continue our investigation of paraorthomodular BZ*-lattices (PBZ * -lattices), started in [18,19,20,21,33]. We shed further light on the structure of the subvariety lattice of the variety PBZL * of PBZ * -lattices; in particular, we provide axiomatic bases for some of its members. Further, we show that some distributive subvarieties of PBZL * are termequivalent to well-known varieties of expanded Kleene lattices or of nonclassical modal algebras. By so doing, we somehow help the reader to locate PBZ * -lattices on the atlas of algebraic structures for nonclassical logics.