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This article is cited in 9 scientific papers (total in 9 papers)
Two-dimensional modal logic
V. B. Shekhtman Moscow State Pedagogical Institute
Abstract:
Propositional 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 $\square_i\square_jp\equiv\square_j\square_ip$ and $\lozenge_i\square_jp\supset\square_j\lozenge_ip$. A special case of this problem, leading to the logic of a torus $S5\times S5$ was solved by Segerberg [1].
Received: 13.02.1975
Citation:
V. B. Shekhtman, “Two-dimensional modal logic”, Mat. Zametki, 23:5 (1978), 759–772; Math. Notes, 23:5 (1978), 417–424
Linking options:
https://www.mathnet.ru/eng/mzm10005 https://www.mathnet.ru/eng/mzm/v23/i5/p759
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