Modal Languages for Topology: Expressivity and Definability

Balder Ten Cate (1) , David Gabelaia (2) , Dmitry Sustretov (3)

1 UNIVERSITY OF AMSTERDAM - ISLA - Informatics Institute
2 RAZMADZE MATHEMATICAL INSTITUTE - Department of Mathematical Logic
3 LANGUE ET DIALOGUE - Human-machine dialogue with a significant language component

In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt-Thomason definability theorem in terms of the well established first-order topological language $L_t$.

Mots clés: modal logic; hybrid logic; topological semantics; correspondence theory; neighborhood semantics; algebraic semantics; Alexandroff spaces; binder; global modality; difference modality

Domaines: Logique [math.LO]

Balder Ten Cate, David Gabelaia, Dmitry Sustretov. Modal Languages for Topology: Expressivity and Definability. 2006. ⟨hal-00105443⟩