Multimo dal Logics of Products of Topologies

Studia Logica 84 (3):369-392 (2006)
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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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Johan Van Benthem
University of Amsterdam

References found in this work

The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Two-dimensional modal logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.
Many-dimensional modal logics: theory and applications.Dov M. Gabbay (ed.) - 2003 - Boston: Elsevier North Holland.
Diodorean modality in Minkowski spacetime.Robert Goldblatt - 1980 - Studia Logica 39 (2-3):219 - 236.

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