Abstract In Osorio et al. [Revisiting Z. Notre Dame Journal of Formal Logic, 55(1):129–155, 2014] introduced a paraconsistent three-valued logic, the logic CG 3 ′ which was named after the logic G 3 ′ due to the close relation between them. Authors defined CG 3 ′ via the three-valued matrix that defines G 3 ′ but changing the set of designated truth values. In this article we present a brief study of the Kripke-type semantics for some logics related with CG 3 ′ before constructing a Kripke-type semantics for it.