Topological Semantics and Decidability

Dmitry Sustretov

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arXiv · math/0703106

Topological Semantics and Decidability

Dmitry Sustretov

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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$. 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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BibTeX RIS

Dmitry Sustretov. 2007-06-01. Topological Semantics and Decidability. https://arxiv.org/abs/math/0703106

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