Studia Logica 104 (3):487-502 (2016)

Philip Kremer
University of Toronto at Scarborough
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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References found in this work BETA

The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
Products of Modal Logics, Part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.
Extensions of the Lewis System S5.Schiller Joe Scroggs - 1951 - Journal of Symbolic Logic 16 (2):112-120.

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Topological-Frame Products of Modal Logics.Philip Kremer - 2018 - Studia Logica 106 (6):1097-1122.

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