Abstract
We consider the modal logics wK4 and DL as well as the corresponding weakly transitive modal algebras and DL-algebras. We prove that there exist precisely 16 amalgamable varieties of DL-algebras. We find a criterion for the weak amalgamation property of varieties of weakly transitive modal algebras, solve the deductive interpolation problem for extensions of the logic of inequality DL, and obtain a weak interpolation criterion over wK4.
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Original Russian Text Copyright © 2010 Karpenko A. V.
The author was supported by the Russian Foundation for Basic Research (Grant 09-01-00090a), the Russian Federal Agency for Education (Grant 2.1.1.419), and the State Maintenance Program for the Young Science Doctors (a Grant of the President of the Russian Federation) (Grant MD-2587.2010.1).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 553–568, May–June, 2010.
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Karpenko, A.V. Interpolation properties in the extensions of the logic of inequality. Sib Math J 51, 439–451 (2010). https://doi.org/10.1007/s11202-010-0045-0
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DOI: https://doi.org/10.1007/s11202-010-0045-0