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

Two-Dimensional Modal Logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.
Products of Modal Logics, Part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.
Dynamic Topological Logic.Philip Kremer & Grigori Mints - 2005 - Annals of Pure and Applied Logic 131 (1-3):133-158.
Reduction of Second‐Order Logic to Modal Logic.S. K. Thomason - 1975 - Mathematical Logic Quarterly 21 (1):107-114.

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On Graph-Theoretic Fibring of Logics.A. Sernadas, C. Sernadas, J. Rasga & M. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1321-1357.

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