Authors
Philip Kremer
University of Toronto at Scarborough
Abstract
Shehtman introduced bimodal logics of the products of Kripke frames, thereby introducing frame products of unimodal logics. Van Benthem, Bezhanishvili, ten Cate and Sarenac generalize this idea to the bimodal logics of the products of topological spaces, thereby introducing topological products of unimodal logics. In particular, they show that the topological product of S4 and S4 is S4 ⊕ S4, i.e., the fusion of S4 and S4: this logic is strictly weaker than the frame product S4 × S4. Indeed, van Benthem et al show that S4 ⊕ S4 is the bimodal logic of the particular product space Q × Q, leaving open the question of whether S4 ⊕ S4 is also complete for the product space R × R. We answer this question in the negative.
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References found in this work BETA

Products of Modal Logics, Part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.

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Citations of this work BETA

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

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