Open AccessTernary Relational Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer's Logic B
Author(s) -
Sandra M. López
Publication year - 2021
Publication title -
bulletin of the section of logic
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.225
H-Index - 13
eISSN - 2449-836X
pISSN - 0138-0680
DOI - 10.18778/0138-0680.2021.16
Subject(s) - soundness , completeness (order theory) , semantics (computer science) , t norm fuzzy logics , mathematics , logical consequence , computer science , programming language , discrete mathematics , theoretical computer science , algebra over a field , pure mathematics , artificial intelligence , mathematical analysis , membership function , fuzzy set , fuzzy logic
Six hopefully 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.