Minds and Machines

, Volume 10, Issue 3, pp 321–360

The Nature of Nonmonotonic Reasoning


  • Charles G. Morgan
    • Department of PhilosophyUniversity of Victoria
    • Varney Bay Institute for Advanced Study

DOI: 10.1023/A:1026560718525

Cite this article as:
Morgan, C.G. Minds and Machines (2000) 10: 321. doi:10.1023/A:1026560718525


Conclusions reached using common sense reasoning from a set of premises are often subsequently revised when additional premises are added. Because we do not always accept previous conclusions in light of subsequent information, common sense reasoning is said to be nonmonotonic. But in the standard formal systems usually studied by logicians, if a conclusion follows from a set of premises, that same conclusion still follows no matter how the premise set is augmented; that is, the consequence relations of standard logics are monotonic. Much recent research in AI has been devoted to the attempt to develop nonmonotonic logics. After some motivational material, we give four formal proofs that there can be no nonmonotonic consequence relation that is characterized by universal constraints on rational belief structures. In other words, a nonmonotonic consequence relation that corresponds to universal principles of rational belief is impossible. We show that the nonmonotonicity of common sense reasoning is a function of the way we use logic, not a function of the logic we use. We give several examples of how nonmonotonic reasoning systems may be based on monotonic logics.

logicnon-classical logicnonmonotonic logic

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© Kluwer Academic Publishers 2000