Abstract
This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual set-theoretical interpretation. (ii) A proof format may display an internal dynamics (defeasible conclusions) in the absence of an external dynamics (non-monotonicity). (iii) A monotonic logic may have a non-monotonic characterization.
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Batens, D. A Dynamic Characterization of the Pure Logic of Relevant Implication. Journal of Philosophical Logic 30, 267–280 (2001). https://doi.org/10.1023/A:1017520011692
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DOI: https://doi.org/10.1023/A:1017520011692