Nonmonotonic reasoning is reasoning in which adding new information can force you to withdraw a conclusion you had already drawn. The name contrasts with classical logic, which is monotonic: in ordinary deduction, once a statement follows from a set of premises it keeps following no matter how many premises you add. Common-sense thought does not behave that way. Told only that Tweety is a bird, you conclude Tweety can fly; told additionally that Tweety is a penguin, you take that conclusion back. The set of beliefs shrank when a fact was added, which is exactly the non-monotonic behavior classical logic forbids.
This concept crystallized around 1980, when the journal Artificial Intelligence devoted a special issue to it. Raymond Reiter’s “A Logic for Default Reasoning,” cited here, formalized default rules of the form “in the absence of information to the contrary, assume X,” and defined the consistent sets of conclusions, called extensions, that such rules generate. John McCarthy’s circumscription, published in the same period, minimized the set of abnormal or exceptional cases so a reasoner could assume things are normal unless told otherwise. Jon Doyle’s truth maintenance systems gave a procedural counterpart, tracking the justifications behind beliefs so that conclusions could be cleanly retracted when their support disappeared.
Nonmonotonic reasoning was the symbolic AI community’s answer to two stubborn obstacles, the frame problem and the qualification problem, both of which arise because no one can state every fact and every exception explicitly. It remains foundational to logic programming with negation-as-failure, to belief revision, and to any system that must act sensibly on incomplete knowledge.
Why a business reader should care: real operations run on defaults that occasionally break (“assume in stock unless flagged”), and nonmonotonic reasoning is the rigorous account of how an automated system can rely on such assumptions while revising them gracefully the moment an exception shows up.