Hennessy-Milner Properties via Topological Compactness

Abstract

We give Hennessy-Milner classes for intuitionistic, dual-intuitionistic and biintuitionistic logic interpreted in intuitionistic Kripke models, and generalise these results to modal (dual-and bi-)intuitionistic logics. Our main technical tools are image-compact and pre-image-compact relations that provide a semantical description of modal saturation properties.