Topological Semantics and Decidability

Dmitry Sustretov (1)

1 TALARIS - Natural Language Processing: representation, inference and semantics

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.

Mots clés: modal logic; hybrid logic; topological semantics; decidability

Domaines: Logique [math.LO]

Dmitry Sustretov. Topological Semantics and Decidability. 2007. ⟨hal-00134914⟩