 Cautious Montony (resp. Cut) states that adding a consequence \(\phi\) to the premise-set \(\Sigma\) does not lead to any decrease (resp. increase) in inferential power. Taken together these principles express that inference is a cumulative enterprise: we can keep drawing consequences that can in turn be used as additional premises, without affecting the set of conclusions. In  Gabbay (1985)  it has been shown that some basic and intuitive assumptions about non-monotonic derivations give rise to consequence relations which satisfy Cautious Monotony, Cut and Reflexivity (If \(\phi \in \Sigma\) then \(\Sigma \nc \phi\)). Accordingly, these properties are commonly taken to be central principles of  NML.[1] 