 Since \(A\not \vDash \neg A &gt;B\), the Cooper conditional blocks one of the paradoxes of the material conditional, but it retains another one, namely \(A\vdash B&gt;A\). Relatedly, although Cooper and Cantwell or Olkhovikov use different semantics for conjunction, on their approaches, conjunction entails the conditional. This principle is called Conjunctive Sufficiency: