The problem of restricted interpolation and definability in normal extensions of modal logic S4 is investigated. We specify necessary conditions for the restricted interpolation property IPR in the systems under consideration, and prove that there exist only finitely many logics possessing IPR or the projective Beth property PB2. These logics are all residually finite and recognizable over S4. As a consequence, the restricted interpolation problem and the projective Beth property are decidable over S4.
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*Supported by RFBR (project No. 12-01-00168a) and by the Russian Ministry of Education through the Analytical Departmental Target Program “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1.10726).
Translated from Algebra i Logika, Vol. 52, No. 4, pp. 461-501, July-August, 2013.
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Maksimova, L.L. Restricted interpolation over modal logic S4. Algebra Logic 52, 308–335 (2013). https://doi.org/10.1007/s10469-013-9244-7
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DOI: https://doi.org/10.1007/s10469-013-9244-7