We consider the lattices of extensions of three logics: (1) modal bilattice logic; (2) full Belnap–Dunn bimodal logic; (3) classical bimodal logic. It is proved that these lattices are isomorphic to each other. Furthermore, the isomorphisms constructed preserve various nice properties, such as tabularity, pretabularity, decidability or Craig’s interpolation property.
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Translated from Algebra i Logika, Vol. 60, No. 6, pp. 612-635, November-December, 2021. Russian DOI: https://doi.org/10.33048/alglog.2021.60.607.
This work was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No. 075-15-2019-1614.
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Speranski, S.O. Modal Bilattice Logic and its Extensions. Algebra Logic 60, 407–424 (2022). https://doi.org/10.1007/s10469-022-09667-x
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DOI: https://doi.org/10.1007/s10469-022-09667-x