Relevance logic and entailment
Version: v1, Published online: 1998
Retrieved June 09, 2023, from https://www.rep.routledge.com/articles/thematic/relevance-logic-and-entailment/v-1
‘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.
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.
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