Translating between the representations of a ranked convex geometry

It is well known that every closure system can be represented by an implicational base, or the set of its meet-irreducible elements. In Horn logic, these are respectively as expressions and characteristic models. this paper, we consider problem translating between two representations in acyclic convex geometries. Quite surprisingly, show context already harder than dualization distributive lattices, a generalization well-known hypergraph for which existence output quasi-polynomial time algorithm open. light result, proper subclass geometries, namely ranked those admit base analogous to posets. For class, provide algorithms based on representations.