Matching Topological and Frame Products of Modal Logics

Studia Logica 104 (3):487-502 (2016)
Abstract
The simplest combination of unimodal logics \ into a bimodal logic is their fusion, \, axiomatized by the theorems of \. Shehtman introduced combinations that are not only bimodal, but two-dimensional: he defined 2-d Cartesian products of 1-d Kripke frames, using these Cartesian products to define the frame product \. Van Benthem, Bezhanishvili, ten Cate and Sarenac generalized Shehtman’s idea and introduced the topological product \, using Cartesian products of topological spaces rather than of Kripke frames. Frame products have been extensively studied, but much less is known about topological products. The goal of the current paper is to give necessary and sufficient conditions for the topological product to match the frame product, for Kripke complete extensions of \
Keywords Bimodal logic  Multimodal logic  Topological semantics  Topological product  Product space
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DOI 10.1007/s11225-015-9648-6
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Schiller Joe Scroggs (1951). Extensions of the Lewis System S5. Journal of Symbolic Logic 16 (2):112-120.

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Philip Kremer (2009). Dynamic Topological S5. Annals of Pure and Applied Logic 160 (1):96-116.

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