A 4-valued logic for double Stone algebras

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 LD of double Stone algebras. Furthermore, the rough set semantics of the logic LD is provided by dividing the boundary region (uncertainty) into two disjoint subregions. •The 4-valued semantics of the logic LD has been investigated.•The logic presented is truly a 4-valued logic.•We have also provided the rough set semantics of the proposed logic.•Finally the logic is shown to be sound and complete.