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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Wolter, F. What is the upper part of the lattice of bimodal logics?. Stud Logica 53, 235–241 (1994). https://doi.org/10.1007/BF01054711
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DOI: https://doi.org/10.1007/BF01054711