Ordinary logic is Monotonic, that is, new facts (axioms) can never invalidate previous deductions. The set of derived facts can only increase.

** Problem:** Real-world problems rarely present
us with a complete set of facts.
Usually, we make assumptions based on what is ``usual''; sometimes these
assumptions are incorrect. Non-monotonic logics attempt to allow
assumptions to be made, an if necessary retracted, while staying within
the framework of logic.

BIRD (x): m FLIES (x) --------------------- FLIES (x)``IF BIRD (x) and it is consistent to assume FLIES (x), then assume FLIES (x).''