A variety of algebras closely related to subordination algebras. Issue 2 (3rd July 2022)

• Record Type: Journal Article
• Authors: Celani, Sergio; Jansana, Ramon
• Is Part Of: Journal of applied non-classical logics. Volume 32:Issue 2/3(2022)
• Page Start: 200
• Page End: 238
• Publication Date: 2022-07-03
• Subjects: Subordination algebras -- precontact algebras -- region-based theory of space -- modal logic; 03B45 -- 03G05 -- 03G25 -- 06E15 -- 06E75; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2022.2109122
• Languages: English
• ISSNs: 1166-3081

Abstract

Abstract : We introduce a variety of algebras in the language of Boolean algebras with an extra implication, namely the variety of pseudo-subordination algebras, which is closely related to subordination algebras. We believe it provides a minimal general algebraic framework where to place and systematise the research on classes of algebras related to several kinds of subordination algebras. We also consider the subvariety of pseudo-contact algebras, related to contact algebras, and the subvariety of the strict implication algebras introduced in Bezhanishvili et al. [(2019). A strict implication calculus for compact Hausdorff spaces. Annals of Pure and Applied Logic, 170, 102714]. The variety of pseudo-subordination algebras is term equivalent to the variety of Boolean algebras with a binary modal operator. We exploit this fact in our study. In particular, to obtain a topological duality from which we derive the known topological dualities for subordination algebras and contact algebras.