Monotonicity: Why Shouldn’t New Information Undo an Old Conclusion?

Monotonicity does not mean that events can only increase. It describes a relation of inference: if a set of premises strictly entails a conclusion, adding further premises does not cancel that conclusion. Suppose “all registered members may enter” and “Xiaolin is a registered member” entail “Xiaolin may enter”. Learning later that Xiaolin is wearing blue changes nothing about that inference.

Everyday judgement, however, is often non-monotonic. From “birds normally fly” and the sight of a bird, we may provisionally infer that it flies. Once we learn that it is a penguin, we should withdraw the conclusion. The original judgement depended on “normally” and incomplete information; it was not strict deduction.

Monotonicity protects the accumulation of demonstrated conclusions. Non-monotonic reasoning allows a judgement to be revised when an exception appears. The difference is not reliability versus unreliability, but the kind of commitment being made: one conclusion survives added premises, while the other is explicitly the best retractable judgement available so far. In AI, law and ordinary life, the crucial first step is to say which kind of inference we are making.

https://plato.stanford.edu/entries/logic-nonmonotonic/