 The only modification that is essential is to drop the condition of Centering (both strong and weak), a condition that makes modus ponens (affirming the antecedent) logically valid. If the conditional \(\Rightarrow\) is to represent a default conditional, we do not want modus ponens to be valid: we do not want \((p \Rightarrow q)\) and \(p\) to entail \(q\) classically (i.e., monotonically). If Centering is dropped, the resulting logic can be made to correspond exactly to either a preferential or a rational defeasible entailment relation. For example, the condition of Rational Monotony is the exact counterpart of the CV axiom of Lewis’s logic: