Abstract
Craig's interpolation theorem fails for the prepositional logicsE of entailment,R of relevant implication andT 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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Urquhart, A. Failure of interpolation in relevant logics. J Philos Logic 22, 449–479 (1993). https://doi.org/10.1007/BF01349560
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DOI: https://doi.org/10.1007/BF01349560