 Suppose that Sophia believes that Verdi is Italian and that Bizet and Satie are both French. Let \(\alpha\) be the sentence that Verdi and Bizet are compatriots. Let \(\beta\) be the belief that Satie is French. Let \(\gamma\) be the sentence that Bizet and Satie are compatriots. Suppose that Sophia receives the evidence \(\alpha\). As a result, she concludes that either Verdi and Bizet are both French, or they are both Italian, but she cannot say which. She retains her belief that Satie is French. So \(\alpha \dproves \beta\) and \(\alpha \not\mkern-7mu\dproves \neg \gamma\). Now suppose that she receives the evidence \(\gamma\). Since \(\gamma\) is compatible with her previous conclusions, Rational Monotonicity requires her to retain belief in \(\beta\) and conclude that all three composers are French. However, it seems perfectly rational to retract \(\beta\) and conclude that the three are either all Italian, or all French. 