Relevant implication and the case for a weaker logic

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