Topological Semantics and Decidability

Abstract

It is well-known that the basic modal logic of all topological spaces is $S4$. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal logics of $T_0$, $T_1$ and $T_2$ topological spaces coincide and are S4$.Wealsoexaminebasichybridlogicsoftheseclassesandprovetheirdecidability;aspartofthis,wefindoutthatthehybridlogicsof$T_1$and{T}_2$ spaces coincide.

presentation changes, results about concrete structure added