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This article is cited in 2 scientific papers (total in 2 papers)
Squares of modal logics with additional connectives
V. B. Shehtmanabc a National Research University "Higher School of Economics"
b Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences
c Moscow State University
Abstract:
This paper studies two-dimensional modal logics of a special type, ‘Segerberg squares’. They are defined as the usual squares of modal logics with additional connectives corresponding to the diagonal symmetry and the two projections onto the diagonal. For these logics a finite axiomatization is constructed in many cases, and completeness and the finite model property are proved. A translation of Segerberg squares into classical predicate logic is constructed.
Bibliography: 21 titles.
Keywords:
modal logic, product of modal logics, Segerberg square, completeness, finite model property, filtration method, classical predicate logic, Entscheidungsproblem.
Received: 10.08.2011
Citation:
V. B. Shehtman, “Squares of modal logics with additional connectives”, Uspekhi Mat. Nauk, 67:4(406) (2012), 129–186; Russian Math. Surveys, 67:4 (2012), 721–777
Linking options:
https://www.mathnet.ru/eng/rm9442https://doi.org/10.1070/RM2012v067n04ABEH004805 https://www.mathnet.ru/eng/rm/v67/i4/p129
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Abstract page: | 580 | Russian version PDF: | 352 | English version PDF: | 24 | References: | 106 | First page: | 28 |
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