Strong Depth Relevance

Australasian Journal of Logic 18 (6):645-656 (2021)
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Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these two properties. I also show how to use this fact to demonstrate that these logics seem to be constructive in previously unknown ways.

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Shay Logan
Kansas State University


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