Topological Semantics and Decidability
نویسنده
چکیده
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 T0, T1 and T2 topological spaces coincide and are S4. We also examine basic hybrid logics of these classes and prove their decidability; as part of this, we find out that the hybrid logics of T1 and T2 spaces coincide.
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