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).
"Connexive Restricted Quantification." Notre Dame J. Formal Logic 61 (3) 383 - 402, September 2020. https://doi.org/10.1215/00294527-2020-0015