2019/10/31 by Giuntini, Roberto, Mureşan, Claudia, Paoli, Francesco
#FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1911.00094
We continue our investigation of paraorthomodular BZ*-lattices (PBZ*-lattices), started in \citeGLP1+,PBZ2,rgcmfp,pbzsums,pbz5. We shed further light on the structure of the subvariety lattice of the variety \mathbbPBZL∗ of PBZ*-lattices; in particular, we provide axiomatic bases for some of its members. Further, we show that some distributive subvarieties of \mathbbPBZL∗ are term-equivalent 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.