 There are several further and some diverging notions of a connexive logic. In particular, the second decade of the 21st century has (unfortunately) seen the introduction of confusingly many new notions of connexivity and non-uniform terminology. McCall (1966) introduced connexive logics as systems ranging from logics in which no proposition implies or is implied by its own negation to logics in which BT is provable (together with non-symmetry of implication), and, similarly, Mares and Paoli (2019) characterize connexive logics as systems having some or all of AT, AT′, BT, and BT′ among their theorems (without explicitly requiring non-symmetry of implication). In McCall 2012, AT′ and BT are said to be the distinguishing marks of connexive logic, but note that AT and BT′ are valid in the system CC1 due to Angell (1962) and MacCall (1966) as well. Logics in which some but not all of AT, AT′, BT, and BT′ are provable (or valid) are called ‘demi-connexive’ in Wansing, Omori, and Ferguson 2016 (without explicitly requiring non-symmetry of implication), and are said to be quasi-connexive in Jarmużek and Malinowski 2019a. The identification of the negation of (A → B) with (A → ~B), ascribed to Boethius by Kneale and Kneale (1962), suggests a strengthening of BT and BT′ to the equivalences: