 Now consider the theory \((\{\theta \vee \gamma\}, \Delta)\). We have two extensions: one the same as before, but also another one coinciding with the deductive closure of \(\{\neg\theta\}\), and hence not containing \(\theta\). It follows that the intersection of the extensions no longer contains \(\theta\), so that \((\{\theta \vee \gamma\}, \Delta) \nc \theta\) fails, against Cautious Monotony. (Notice that the same example establishes a counter-example for Cut for the credulous strategy, when we pick the extension of \((\{\theta \vee \gamma\}, \Delta)\) that contains \(\neg\theta\).) 