"Consider putting an axiom in a common sense database asserting that birds can fly. Clearly the axiom must be qualified in some way since penguins, dead birds and birds whose feet are encased in concrete can't fly. A careful construction of the axiom might succeed in including the exceptions of penguins and dead birds, but clearly we can think up as many additional exceptions like birds with their feet encased in concrete as we like. Formalized nonmonotonic reasoning [citations] provides a way of saying that a bird can fly unless there is an abnormal circumstance and reasoning that only the abnormal circumstances whose existence follows from the facts being taken into account will be considered." -John McCarthy

Nonmonotonicity.By John McCarthy.

Non-Monotonic Logic. Entry in The Stanford Encyclopedia of Philosophy by Aldo Antonelli (Summer 2003 Edition), Edward N. Zalta (ed.). "The term 'non-monotonic logic' covers a family of formal frameworks devised to capture and represent defeasible inference, i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called 'non-monotonic' because the set of conclusions warranted on the basis of a given knowledge base does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is in contrast to classical (first-order) logic, whose inferences, being deductively valid, can never be 'undone' by new information. ... One of the most significant developments both in logic and artificial intelligence, is the emergence of a number of non-monotonic formalisms, devised expressly for the purpose of capturing defeasible reasoning in a mathematically precise manner. The fact that patterns of defeasible reasoning have been accounted for in such a rigorous fashion has wide-ranging consequences for our conceptual understanding of argumentation and inference."

Nonmonotonic Logics. In MIT Encyclopedia of Cognitive Science (1999). Entry by Leora Morgenstern.

Non-monotonic Logic. From Anthony Aaby, Walla Walla College Computer Science Department. Here's a good opportunity to see the language of logic.

• and there's even more for you at his site: The Logical Foundations of Computer Science and Mathematics.

Non-monotonic and defeasible logics. From Building Intelligent Legal Information Systems: Representation and Reasoning in Law. By John Zeleznikow and Dan Hunter. "Where we have a set of axioms defined in the logical language, adding new axioms or facts may increase the set of true statements or may leave the set unchanged. However in no case would the addition of new statements reduce the number of true statements in the set of predicates. This feature is known as the monotonicity of the logic. It means that the logic is indefeasible, that there is no situation where the statement p Æ q can be defeated by further information. ... However in human reasoning, and particularly in law, we often find that the existence of both p Æ q and p does not necessarily entail q. We often have special exceptional cases defined either in statutes or resulting from cases interpreting statutes."

Introduction to Artificial Intelligence LECTURE 11: Nonmonotonic Reasoning. (29 slides.) From the School of Computer Science and Engineering at The Hebrew University of Jerusalem.

"The International Workshops on Nonmonotonic Reasoning (NM) aim to bring together active researchers interested in the area of nonmonotonic reasoning to discuss current research, results, and problems of both a theoretical and practical nature. The field of nonmonotonic reasoning includes work on circumscription, autoepistemic and default logic, truth maintenance, closed-world databases, logic programming, probabilistic reasoning, and related systems. The theory of nonmonotonic reasoning has helped provide a clear and formal framework that can be used to understand and compare issues in action representation, planning, and other areas."