Review of Symbolic Logic 13 (2):436-457 (2020)

Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to an argument when it contributes to the validity of that argument. I then argue that the sequents which best embody this ideal of relevance are the so-called perfect sequents—that is, sequents which are valid but have no proper subsequents that are valid. Church’s theorem entails that there is no recursively axiomatizable proof-system that proves all and only the perfect sequents, so the project that emerges from studying perfection in classical logic is not one of finding a perfect subsystem of classical logic, but is rather a comparative study of classifying subsystems of classical logic according to how well they approximate the ideal of perfection.
Keywords relevance  perfect sequents  classical logic
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DOI 10.1017/s1755020318000382
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References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
Difference-Making Grounds.Stephan Krämer & Stefan Roski - 2017 - Philosophical Studies 174 (5):1191-1215.
Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
Tautological Entailments.Alan Ross Anderson & Nuel D. Belnap - 1962 - Philosophical Studies 13 (1-2):9 - 24.
LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Pavel Arazim & Tomáš Lavička (eds.), The Logica Yearbook 2016. London: College Publications.

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Deep Fried Logic.Shay Allen Logan - forthcoming - Erkenntnis:1-30.

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