A companion to Brady's 4-valued relevant logic BN4: The 4-valued logic of entailment E4

Abstract

Brady's logic BN4 can be viewed as the 4-valued logic of the relevant conditional. The aim of this article is to introduce the logic E4, which can be regarded as the 4-valued logic of (relevant) entailment on the basis of the two following facts: (1) as the logic R-mingle, E4 has the ‘quasi-relevance property’; (2) as Anderson and Belnap's logic of entailment E, E4 encloses a sound theory of logical necessity when the necessity operator is introduced via the definition □A=df(A→A)→A .