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Relevance logic as a conservative extension of classical logic

Makinson, David C. (2014) Relevance logic as a conservative extension of classical logic. In: Hansson, Sven Ove, (ed.) David Makinson on Classical Methods for Non-Classical Problems. Outstanding contributions to logic (Vol.3). Springer, Dordrecht, Netherlands, pp. 383-398. ISBN 9789400777583

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Identification Number: 10.1007/978-94-007-7759-0_17


Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining a suitable closure relation out of the set of theses of relevance logic; the other is by adding to the usual natural deduction system for it further rules with ‘projective constraints’, whose application restricts the subsequent application of other rules. The significance of the two constructions is also discussed.

Item Type: Book Section
Official URL:
Additional Information: © 2014 Springer Science+Business Media Dordrecht
Divisions: Philosophy, Logic and Scientific Method
Subjects: B Philosophy. Psychology. Religion > BC Logic
Date Deposited: 20 Aug 2013 14:34
Last Modified: 20 Oct 2021 01:18

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