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Article

Squares of modal logics with additional connectives

Russian Mathematical Surveys. 2012. Vol. 67. No. 4. P. 721-777.
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.