  In this paper we introduce the class of weak Heyting Brouwer algebras
(WHB-algebras, for short). We extend the well known duality between
distributive lattices and Priestley spaces, in order to exhibit a relational
Priestley-like duality for WHB-algebras. Finally, as an application of the
duality, we build the tense extension of a WHB-algebra and we employ it as a
tool for proving structural properties of the variety such as the finite model
property, the amalgamation property, the congruence extension property and the
Maehara interpolation property.
