Some constructive variants of S4 with the finite model property - Balbiani, Philippe; Dieguez, Martin; Fernandez-Duque, David (Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, 2021)
The logics CS4 and IS4 are intuitionistic variants of the modal logic S4. Whether the finite model property holds for each of these logics has been a long-standing open problem. In this paper we introduce two logics closely related to IS4: GS4, obtained by adding the Gödel-Dummett axiom to IS4, and S4I, obtained by reversing the roles of the modal and intuitionistic relations. We then prove that CS4, GS4, and S4I all enjoy the finite model property.