A 2 Set-up Ternary Relational Semantics for the Companions to Brady’s 4-valued logic BN4

Abstract

The present paper is inspired by Ross T. Brady’s work on semantics for many-valued logics which also belong to the family of relevance. In particular, we aim to enhance his methodology for (meta)completeness results with respect to a 2 set-up ternary relational semantics. In 1982, Brady developed the 4-valued logic BN4 and endowed it with such semantics, providing both strong soundness and completeness theorems. In the recent literature, six new 4-valued logics have been defined as companions to the system BN4 and endowed with a bivalent Belnap-Dunn type semantics. The aim of this paper is to deepen the knowledge of these new companions to BN4 by providing a 2 set-up ternary relational semantics, thus following the same strategies Brady applied to BN4 in (Brady, 1982).