Show Summary Details

Page of

PRINTED FROM OXFORD REFERENCE (www.oxfordreference.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single entry from a reference work in OR for personal use (for details see Privacy Policy and Legal Notice).

date: 23 July 2021

relevant logic

A Dictionary of Logic

Thomas Macaulay Ferguson,

Graham Priest

relevant logic 

Describes a deductive system that satisfies the variable sharing property, so that whenever relevant logic is a logical truth (or a theorem), relevant logic and relevant logic have at least one propositional variable in common. Motivated by the paradoxes of relevance, relevant logics were formulated by Alan Anderson (1925–1973) and Nuel Belnap (1930– ), drawing on the work of Wilhelm Ackermann (1896–1962) and Alonzo Church (1903–1995). There are several different semantics for relevant logics, but the most popular is the one developed by Richard Sylvan (né Routley) (1935–1996) and Robert Meyer (1932–2009). This is a world-semantics. It uses the Routley star to give the semantics for negation, and a ternary relation, relevant logic, to give the truth conditions for the conditional, as follows:

  • relevant logic is true at world relevant logic iff for all worlds, relevant logic and relevant logic such that relevant logic, if relevant logic is true at relevant logic, relevant logic is true at relevant logic.

The philosophical meaning of the ternary relation is contested. As for the binary accessibility relation of modal logic, putting various constraints on the relevant logic delivers a variety of different relevant logics.