However, these correspondences come at a price. Jarmużek and Malinowski point out that imposing negation closure validates the otherwise refutable formula ~((A →w B) ∧ ~B ∧ ~(~A →w ~B)) with respect to any relation R. Jarmużek and Malinowski also show that these five conditions are independent of each other and therefore give rise to 25 different logics. The two connexive ones (alias properly connexive ones in Jarmużek and Malinowski’s terminology), i.e., the logic defined by means of conditions