De Morgan Algebras with a Quasi-Stone Operator

Blyth, T. S.; Fang, Jie; Wang, Lei-Bo

doi:10.1007/s11225-013-9538-8

Cited by 2 publications

(4 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We begin this section by showing that the variety of antiortholattices generated by the algebra D 5 coincides with the variety of Kleene-Stone algebras. This fact explains the similarity of some results independently obtained in [6,19,33].…”

Section: Comparison With Other Structures 41 Distributive Lattices Wi...supporting

confidence: 90%

“…Bounded distributive lattices expanded both by a De Morgan complementation and a unary operation with Stone-like properties have been the object of rather intensive investigations over the past decades. In particular, Blyth, Fang and Wang [6] have studied, under the label of quasi-Stone De Morgan algebras, bounded distributive lattices with two unary operations that make their appropriate reducts, at the same time, De Morgan algebras and quasi-Stone algebras [37,17,13]. Quasi-Stone De Morgan algebras that are simultaneously Stone algebras and Kleene algebras are known under the name of Kleene-Stone algebras; they have been studied in [25] and, more recently, in the already quoted [6].…”

Section: Comparison With Other Structures 41 Distributive Lattices Wi...mentioning

confidence: 99%

“…In particular, Blyth, Fang and Wang [6] have studied, under the label of quasi-Stone De Morgan algebras, bounded distributive lattices with two unary operations that make their appropriate reducts, at the same time, De Morgan algebras and quasi-Stone algebras [37,17,13]. Quasi-Stone De Morgan algebras that are simultaneously Stone algebras and Kleene algebras are known under the name of Kleene-Stone algebras; they have been studied in [25] and, more recently, in the already quoted [6]. We begin this section by showing that the variety of antiortholattices generated by the algebra D 5 coincides with the variety of Kleene-Stone algebras.…”

Section: Comparison With Other Structures 41 Distributive Lattices Wi...mentioning

confidence: 99%

“…Lemma 31 [6] If A is a quasi-Stone De Morgan algebra, then for all a ∈ A we have that a ∼∼ = a ∼′∼′ .…”

Section: Comparison With Other Structures 41 Distributive Lattices Wi...mentioning

confidence: 99%

See 3 more Smart Citations

On PBZ*-lattices

Giuntini,

Mureşan,

Paoli

2019

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Comparison With Other Structures 41 Distributive Lattices Wi...supporting

confidence: 90%