  In this paper we develop an almost general process to switch from abstract
logics in the sense of Brown and Suszko to lattices. With this method we can
establish dualities between some categories of abstract logics to the
correspondent topological space categories. In more detail we will explain the
duality between the category of abstract intuitionistic logics with
intuitionistic morphisms and the category of Esakia spaces with the Esakia
morphisms.
