Abstract Over the past few years, a new cluster of abstract algebras has emerged within the general context of research in rough set theory. Among them, one is the weakly topological quasi-Boolean algebra. This paper studies the vicinity of weakly topological quasi-Boolean algebra from algebraic and logical perspectives. The weak pre-rough algebra is defined, and a cluster of intermediate algebras between it and the quasi-Boolean algebra is explored. The interrelationship and independence among them are presented. We also establish sound and complete sequential systems for these algebras. Further, we show the finite model property and construct decidable algorithms for weakly topological quasi-Boolean algebra and its weaker variants by context-free grammars. Rough set models of some of these algebras have been presented.
Wang et al. (Sat,) studied this question.