What is the upper part of the lattice of bimodal logics?

Studia Logica 53 (2):235 - 241 (1994)

Abstract
We define an embedding from the lattice of extensions ofT into the lattice of extensions of the bimodal logic with two monomodal operators 1 and 2, whose 2-fragment isS5 and 1-fragment is the logic of a two-element chain. This embedding reflects the fmp, decidability, completenes and compactness. It follows that the lattice of extension of a bimodal logic can be rather complicated even if the monomodal fragments of the logic belong to the upper part of the lattice of monomodal logics.
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DOI 10.1007/BF01054711
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Properties of Independently Axiomatizable Bimodal Logics.Marcus Kracht & Frank Wolter - 1991 - Journal of Symbolic Logic 56 (4):1469-1485.
Normal Forms in Modal Logic.Kit Fine - 1975 - Notre Dame Journal of Formal Logic 16 (2):229-237.
The Lattice of Modal Logics: An Algebraic Investigation.W. J. Blok - 1980 - Journal of Symbolic Logic 45 (2):221-236.
That All Normal Extensions of S4.3 Have the Finite Model Property.R. A. Bull - 1966 - Mathematical Logic Quarterly 12 (1):341-344.
Modal Logics with Functional Alternative Relations.Krister Segerberg - 1986 - Notre Dame Journal of Formal Logic 27 (4):504-522.

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