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arXiv · 1911.00094

On PBZ*-lattices

Roberto Giuntini·Claudia Mureşan·Francesco Paoli
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Abstract

We continue our investigation of paraorthomodular BZ*-lattices (PBZ*-lattices), started in \cite{GLP1+,PBZ2,rgcmfp,pbzsums,pbz5}. We shed further light on the structure of the subvariety lattice of the variety $\mathbb{PBZL}^{\ast }$ of PBZ*-lattices; in particular, we provide axiomatic bases for some of its members. Further, we show that some distributive subvarieties of $\mathbb{PBZL}^{\ast }$ 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.

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Roberto Giuntini, Claudia Mureşan, Francesco Paoli. 2019-10-31. On PBZ*-lattices. https://arxiv.org/abs/1911.00094

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