Connexive Restricted Quantification

Abstract

This paper investigates the meaning of restricted quantification (RQ) (also known as binary quantification) when the embedded conditional (implication) is taken as the conditional of some first-order connexive logics. The study is carried out by checking the suitability of RQ for defining a connexive class theory, in analogy to the definition of Boolean class theory by using RQ in classical logic (embedding the material implication). Negative results are obtained for Wansing’s first-order connexive logic QC and one variant of Priest’s first-order connexive logic QP (based on the null account for paraconsistent logical consequence). A positive result is obtained for another variant of QP (based on the partial account for paraconsistent logical consequence).