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. In this paper, we axiomatize the topological product of S4 and S5, which is strictly between S4 ⊗ S5 and S4 × S5. We also apply our techniques to (1) proving a conjecture of van Benthem et al concerning the logic of products of Alexandrov spaces with arbitrary topological spaces; and (2) solving a problem in quantified modal logic: in particular, it is known that standard quantified S4 without identity, QS4, is complete in Kripke semantics with expanding domains; we show that QS4 is complete not only in topological semantics with constant domains (which was already shown by Rasiowa and Sikorski), but wrt the topological space Q with a constant countable domain.
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References found in this work BETA

The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
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

On Neighbourhood Product of Some Horn Axiomatizable Logics.Andrey Kudinov - 2018 - Logic Journal of the IGPL 26 (3):316-338.
Topological-Frame Products of Modal Logics.Philip Kremer - 2018 - Studia Logica 106 (6):1097-1122.

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