Symmetry Tense Heyting Algebras

Studies in Logic, Vol. 15, No. 3 (2022): 18–35   PII: 1674-3202(2022)-03-0018-18

Xue Ge

Abstract.

In this paper we introduce the class of symmetry tense Heyting algebras (sIK.t-algebras), which is a S4 extension of Ewald’s intuitionistic tense logic. We present the Hilbert axiomatization for sIK.t. Further we show the finite model property (FMP) for the logic of sIK.t-algebras. The result is proved by proof theory and algebraic model theory, using the sequent systems introduced by the present paper.