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Relevance logic and entailment

DOI
10.4324/9780415249126-Y040-1
DOI: 10.4324/9780415249126-Y040-1
Version: v1,  Published online: 1998
Retrieved November 17, 2019, from https://www.rep.routledge.com/articles/thematic/relevance-logic-and-entailment/v-1

Article Summary

‘Relevance logic’ came into being in the late 1950s, inspired by Wilhelm Ackermann, who rejected certain formulas of the form A→B on the grounds that ‘the truth of A has nothing to do with the question whether there is a logical connection between B and A’.

The central idea of relevance logic is to give an account of logical consequence, or entailment, for which a connection of relevance between premises and conclusion is a necessary condition. In both classical and intuitionistic logic, this condition is missing, as is highlighted by the validity in those logics of the ‘spread law’, A &∼A→B; a contradiction ‘spreads’ to every proposition, and simple inconsistency is equivalent to absolute inconsistency. In relevance logic the spread law fails, and the simple inconsistency of a theory (that a set of formulas entails a contradiction) is distinguished from absolute inconsistency (or triviality: that a set of formulas entails every proposition). The programme of relevance logic is to characterize a logic, or a range of logics, satisfying the relevance condition, and to study theories based on such logics, such as relevant arithmetic and relevant set theory.

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Citing this article:
Read, Stephen. Relevance logic and entailment, 1998, doi:10.4324/9780415249126-Y040-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/relevance-logic-and-entailment/v-1.
Copyright © 1998-2019 Routledge.

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