Products of 'transitive' modal logics

Journal of Symbolic Logic 70 (3):993-1021 (2005)
Abstract
We solve a major open problem concerning algorithmic properties of products of ‘transitive’ modal logics by showing that products and commutators of such standard logics as K4, S4, S4.1, K4.3, GL, or Grz are undecidable and do not have the finite model property. More generally, we prove that no Kripke complete extension of the commutator [K4,K4] with product frames of arbitrary finite or infinite depth (with respect to both accessibility relations) can be decidable. In particular, if
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DOI 10.2178/jsl/1122038925
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References found in this work BETA
Dynamic Topological Logic.Philip Kremer & Grigori Mints - 2005 - Annals of Pure and Applied Logic 131 (1-3):133-158.
Products of Modal Logics, Part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.
Reduction of Second‐Order Logic to Modal Logic.S. K. Thomason - 1975 - Mathematical Logic Quarterly 21 (1):107-114.
A Decidable Temporal Logic of Parallelism.Mark Reynolds - 1997 - Notre Dame Journal of Formal Logic 38 (3):419-436.

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