We study the interpolation and Beth definability problems in propositional extensions of minimal logic J. Previously, all J-logics with the weak interpolation property (WIP) were described, and it was proved that WIP is decidable over J. In this paper, we deal with so-called well-composed J-logics, i.e., J-logics satisfying an axiom (⊥ → A) ∨ (A → ⊥). Representation theorems are proved for well-composed logics possessing Craig’s interpolation property (CIP) and the restricted interpolation property (IPR). As a consequence, we show that only finitely many well-composed logics share these properties and that IPR is equivalent to the projective Beth property (PBP) on the class of well-composed J-logics.
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Translated from Algebra i Logika, Vol. 51, No. 2, pp. 244-275, March-April, 2012.
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Maksimova, L.L. Interpolation and the projective Beth property in well-composed logics. Algebra Logic 51, 163–184 (2012). https://doi.org/10.1007/s10469-012-9180-y
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DOI: https://doi.org/10.1007/s10469-012-9180-y