Continua of Logics Related to Intuitionistic and Minimal Logics

Abstract

We analyze the relationship between logics around intuitionistic logic and minimal logic. We characterize the intersection of minimal logic and co-minimal logic introduced by Vakarelov, and reformulate logics given in the previous studies by Vakarelov, Bezhanishvili, Colacito, de Jongh, Vargas, and Niki in a uniform language. We also compare the new logic with other known logics in terms of the cardinalities of logics between them. Specifically, we apply Wronski’s algebraic semantics, instead of neighborhood semantics used in the previous studies, to show the existence of continua of logics between known logics and the new logic. This result is an extension of the conventional results, and the proof is given in a simpler way.