A 4-valued logic for double Stone algebras

Abstract

This paper investigates the logical structure of the 4-element chain considered as a double Stone algebra. It has been shown that any element of a double Stone algebra can be identified as monotone ordered triplet of sets. As a consequence, we obtain the 4-valued semantics for the logic L<inf>D</inf> of double Stone algebras. Furthermore, the rough set semantics of the logic L<inf>D</inf> is provided by dividing the boundary region (uncertainty) into two disjoint subregions. © 2024 Elsevier Inc.