Failure of interpolation in relevant logics

Journal of Philosophical Logic 22 (5):449 - 479 (1993)
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Abstract

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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2009-01-28

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Alasdair Urquhart
University of Toronto, St. George Campus

Citations of this work

A plea for KR.Alison Duncan Kerr - 2019 - Synthese 198 (4):3047-3071.
Relevant implication and the case for a weaker logic.Ross T. Brady - 1996 - Journal of Philosophical Logic 25 (2):151 - 183.
Duality for algebras of relevant logics.Alasdair Urquhart - 1996 - Studia Logica 56 (1-2):263 - 276.
Modal translations in substructural logics.Kosta Došen - 1992 - Journal of Philosophical Logic 21 (3):283 - 336.
The relevant fragment of first order logic.Guillermo Badia - 2016 - Review of Symbolic Logic 9 (1):143-166.

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References found in this work

The undecidability of entailment and relevant implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.
Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.
Entailment. Vol. 1.Alan Ross Anderson & Nuel D. Belnap - 1977 - Canadian Journal of Philosophy 7 (2):405-411.

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