Failure of interpolation in relevant logics

Journal of Philosophical Logic 22 (5):449 - 479 (1993)
Craig's interpolation theorem fails for the propositional logics E of entailment, R of relevant implication and T of ticket entailment, as well as in a large class of related logics. This result is proved by a geometrical construction, using the fact that a non-Arguesian projective plane cannot be imbedded in a three-dimensional projective space. The same construction shows failure of the amalgamation property in many varieties of distributive lattice-ordered monoids
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    Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
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