Modal Logics for Products of Topologies
Johan van Benthem, Guram Bezhanishvili, Balder ten Cate, Darko Sarenac
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 topological
spaces with horizontal, vertical, and standard product topologies. We
prove that both of these logics are complete for the product of
rational numbers Q x Q with the appropriate topologies.