 The remaining principles are the heart of System P. Cut says that adding conclusions defeasibly inferred from \(\alpha \) to the premises does not increase inferential power. Cautious Monotonicity says that it does not decrease inferential power. Let \(C(\alpha)\) be \( \{ \beta : \alpha \dproves \beta \} \), the set of conclusions licensed by \(\alpha\). If we think of the premise on the left of \(\dproves\) as expressing my total “hard” evidence, and the set \(C(\alpha)\) as a theory inductively inferred on the basis of \(\alpha\), then Cautious Monotonicity is an expression of hypothetico-deductivism: if I learn a consequence of my theory \(C(\alpha)\), I should not retract any of my previous conclusions. Moreover, Cut says that I should not add any new conclusions. Taken together, the two principles say that if a consequence of your theory is added to your total evidence, your theory should not change, i.e. if \(\alpha\dproves \beta\), then \(C(\alpha)=C(\alpha\wedge \beta)\). 