Relevant implication and the case for a weaker logic

Journal of Philosophical Logic 25 (2):151 - 183 (1996)
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Abstract

We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for $DJ^{d}$ with respect to a content semantics, which embraces the concept of meaning containment

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Citations of this work

Assertion, denial and non-classical theories.Greg Restall - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 81--99.
Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General.Ross T. Brady - 2017 - IfCoLog Journal of Logics and Their Applications 4 (3):755--781.
What is Wrong with Cantor's Diagonal Argument?R. T. Brady & P. A. Rush - 2008 - Logique Et Analyse 51 (1):185-219..

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References found in this work

Universal Logic.Ross Brady - 2006 - CSLI Publications.
Universal Logic.Ross Brady - 2006 - Bulletin of Symbolic Logic 13 (4):544-547.
Models for entailment.Kit Fine - 1974 - Journal of Philosophical Logic 3 (4):347 - 372.
The undecidability of entailment and relevant implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.

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