Derivational Modal Logics with the Difference Modality
This is a chapter in a book dedicated to Leo Esakia’s contributions to the theory of modal and intuitionistic systems. In this chapter we study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces, T1 -spaces, dense-in-themselves spaces, a zero-dimensional dense-in-itself separable metric space, R^n (n ≥ 2). We also discuss the correlation between languages with different combinations of the topological, the derivational, the universal and the difference modality in terms of definability.