Ternary Relational Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer's Logic B

• Published in: Bulletin of the Section of Logic Vol. 51; no. 1; pp. 27 - 56
• Main Author: López, Sandra M
• Format: Journal Article
• Language: English
• Published: Warsaw Wydawnictwo Uniwersytetu Łódzkiego 01-01-2022; Lodz University Press; University of Łódź
• Subjects: 4-valued logics; 4-valued quasi-relevant logics; Logic; relevant logics; routley and meyer's logic b; Semantics; ternary relational semantics; relevant logics; 4valued quasirelevant logics; Ternary relational semantics; 4valued logics; Routley and Meyer's logic B
• ISSN: 0138-0680; 2449-836X
• DOI: 10.18778/0138-0680.2021.16

Six interesting variants of the logics BN4 and E4—which can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively—were previously developed in the literature. All these systems are related to the family of relevant logics and contain Routley and Meyer's basic logic B, which is well-known to be specifically associated with the ternary relational semantics. The aim of this paper is to develop reduced general Routley-Meyer semantics for them. Strong soundness and completeness theorems are proved for each one of the logics.