 The systems C and QC are connexive but not Kapsner strong. This is hardly surprising because these logics are paraconsistent and allow formulas A and ~A to be simultaneously satisfiable in the sense that a state and all its possible expansions may support the truth of both A and ~A. As a result, A → ~A and ~A → A are satisfiable. If A → ~A and ~A → A are unsatisfiable, strong connexivity is in conflict with at the same time satisfying the deduction theorem and defining semantical consequence as preservation of support of truth: A → ~A would entail ~(A → ~A), ~A → A would entail ~(~A → A), and the formulas (A → ~A) → ~(A → ~A) and (~A → A) → ~(~A →A) would be valid instead of unsatisifable.