Studia Logica 84 (3):369-392 (2006)

Authors
Johan Van Benthem
University of Amsterdam
Abstract
We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.
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DOI 10.1007/s11225-006-9013-x
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Topology and Measure in Logics for Region-Based Theories of Space.Tamar Lando - 2018 - Annals of Pure and Applied Logic 169 (4):277-311.

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