Lewisian Connexive Logics

Studies in Logic, Vol. 18, No. 3 (2025): 96–114                   PII: 1674-3202(2025)-03-0096-19

Chen Huang, Xuefeng Wen

Abstract. In connexive logic, two fundamental ideas are observed: first, no proposition implies or is implied by its own negation; second, if a proposition implies φ then it will not imply the negation of φ. In classical logic, neither of the ideas holds, which makes it difficult to give a natural semantics for connexive logic. By combining Kleene’s three valued logic and Lewis’ conditional logic, we propose a new natural semantics for connexive logic. We give four axiomatic systems characterizing different classes of selection models in the new semantics. We prove soundness and completeness of these logics and compare them with some connexive logics in the literature.