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

Johan Van Benthem
University of Amsterdam
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 ${\bf S4}\oplus {\bf S4}$ . 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 ${\Bbb Q}\times {\Bbb Q}$ with the appropriate topologies
Keywords Fusion of modal logics  products of modal logics  topological product  horizontal  vertical topologies
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DOI 10.1007/s11225-006-9013-x
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References found in this work BETA

Two-Dimensional Modal Logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Diodorean Modality in Minkowski Spacetime.Robert Goldblatt - 1980 - Studia Logica 39 (2-3):219 - 236.

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Citations of this work BETA

Quantified Modal Logic on the Rational Line.Philip Kremer - 2014 - Review of Symbolic Logic 7 (3):439-454.

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