Topological Semantics and Decidability

Details Topological Semantics and Decidability Topological Semantics and Decidability

2007-03-05

arxiv.org/abs/math/0703106v3

Mathematics

Logic

presentation changes, results about concrete structure added

Scientific paper

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$. 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 $T_1$ and T_2$ spaces coincide.

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