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