Modal Equivalence and Bisimilarity in Many-valued Modal Logics with Many-valued Accessibility Relations

In this paper we investigate the Hennessy-Milner property for models of many-valued modal logics defined based on complete MTL-chains having many-valued accessibility relations. Our main result gives a necessary and sufficient algebraic condition for the class of image-finite models for such modal logics to admit the Hennessy-Milner property.