 The system C is a conservative extension of positive intuitionistic logic. In C, strong negation is interpreted in such a way that it turns the intuitionistic implication of its negation-free sublanguage into a connexive implication. Analogously, strong negation may be added to positive dual intuitionistic logic to obtain a system with a connexive co-implication, and to bi-intuitionistic logic, or to the logic 2Int from Wansing 2016a that also contains an implication and a co-implication connective, to obtain systems with both a connexive implication and a connexive co-implications, see Wansing 2008, 2016b, and Kamide and Wansing 2016.