Abstract

We continue our investigation of paraorthomodular BZ*-lattices PBZ*-lattices, started in Giuntini et al., Mureşan. We shed further light on the structure of the subvariety lattice of the variety PBZL∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {PBZL}^{\mathbb {*}}$$\end{document} of PBZ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{*}$$\end{document}–lattices; in particular, we provide axiomatic bases for some of its members. Further, we show that some distributive subvarieties of PBZL∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {PBZL}^{\mathbb {*}}$$\end{document} are term-equivalent to well-known varieties of expanded KleeneKleene, C. lattices or of nonclassical modal algebrasNonclassical modal algebras. By so doing, we somehow help the reader to locate PBZ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{*}$$\end{document}–lattices on the atlas of algebraic structures for nonclassical logics.