Non-monotonic logic

Non-monotonic logic is a family of formal reasoning systems that allow conclusions to be withdrawn when new information is acquired. Unlike classical logic, in which adding premises can only increase the set of valid conclusions (monotonicity), non-monotonic logics model the human capacity to make defeasible inferences — conclusions that are reasonable given current knowledge but may be overturned by future evidence.

The need for non-monotonic reasoning arises in any domain where agents must act with incomplete information. A bird that cannot fly is typically a penguin, not a violation of physics. A meeting that has not been canceled is assumed to be happening, though it might have been canceled without our knowledge. These are default inferences: conclusions that hold unless defeated by specific counter-evidence.

The field emerged from artificial intelligence research in the 1980s, driven by the need to formalize common-sense reasoning. Key formalisms include default logic, autoepistemic logic, and circumscription. Each provides a mechanism for drawing provisional conclusions while preserving the capacity to revise them. Non-monotonic logic is central to the formal study of the frame problem in epistemology and connects to broader questions in epistemology about the nature of defeasible justification.