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

Sandra M. López

doi:10.18778/0138-0680.2021.16

Authors

Sandra M. López Universidad de Salamanca, Departamento de Filosofía, Lógica y Estética, 37007, Campus Unamuno, Edificio FES, Salamanca, Spain Author https://orcid.org/0000-0003-2584-5950

DOI:

https://doi.org/10.18778/0138-0680.2021.16

Keywords:

Ternary relational semantics, relevant logics, 4-valued logics, Routley and Meyer's logic B, 4-valued quasi-relevant logics

Abstract

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.

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