Abstract
Prepositional logics with many modalites, characterized by “two-dimensional” Kripke models, are investigated. The general problem can be formulated as follows: from two modal logics describing certain classes of Kripke modal lattices construct a logic describing all products of Kripke lattices from these classes. For a large number of cases such a logic is obtained by joining to the original logics an axiom of the form □i□jp ≡ □j□ip and ◊i□jp ⊃ □j◊jp. A special case of this problem, leading to the logic of a torus S5×S5 was solved by Segerberg [1].
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Translated from Matematieheskie Zametki, Vol. 23, No. 5, pp. 759–772, May, 1978.
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Shekhtman, V.B. Two-dimensional modal logic. Mathematical Notes of the Academy of Sciences of the USSR 23, 417–424 (1978). https://doi.org/10.1007/BF01789012
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DOI: https://doi.org/10.1007/BF01789012