  In this article, we continue the study of tense symmetric Heyting algebras
(or TSH-algebras). These algebras constitute a generalization of tense
algebras. In particular, we describe a discrete duality for TSHalgebras bearing
in mind the results indicated by E. Or lowska and I. Rewitzky in [E. Or lowska
and I. Rewitzky, Discrete Dualities for Heyting Algebras with Operators, Fund.
Inform. 81 (2007), no.1-3, 275-295.] for Heyting algebras. In addition, we
introduce a propositional calculus and prove this calculus has TSH-algebras as
algebraic counterpart. Finally, the duality mentioned above allowed us to show
the completeness theorem for this calculus.
