ABSTRACT
Linguistics.—The term relevance is used in logic in a technical sense (→ LOGIC). It is also at the heart of pragmatic views of language and communication (→COMMUNICATION, LANGUAGE, PRAGMATICS).
Relevance logic (also called relevant logic) appeared in the 1950s in direct connection with the desire to propose a new and stronger definition of material implication. In a material implication relation, a proposition if p, then q is true both when p is false, and when p is true and q is also true. When p is true and q is false, the proposition is false. One possible criticism of this classical definition of implication is that p and q do not have to be related semantically or otherwise because it is based solely on the truth or falsity of p and q (→SEMANTICS, TRUTH). To overcome this difficulty (extremely troublesome if one hopes to use logic to account for linguistic behavior, particularly natural-language conditionals), logicians like Alan Anderson and Nuel Belnap developed relevance logic. Basically, there are two foundations of relevance logic: first, p and q must share variables, that is, there must be a semantic link between their prepositional contents; second, there must be a dependency between p and q, in the sense that p must actually be used to obtain q in a relation of entailment. Note that while relevance logic now ranks among the newer widely accepted logics, it has still not achieved its ambition of replacing classical logic in the formalization of natural language.
