IngentaConnect The Nature of Nonmonotonic Reasoning

Author: Morgan C.G.¹

Source: Minds and Machines, Volume 10, Number 3, August 2000 , pp. 321-360(40)

Publisher: Springer

Abstract:

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.

Keywords: logic; non-classical logic; nonmonotonic logic

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Philosophy, University of Victoria, Victoria, B.C. V8W 3P4, Canada and Varney Bay Institute for Advanced Study, P.O. Box 45, Coal Harbour, B.C. VON 1KO, Canada (E-mail: morgan@phastf.phys.uvic.ca)

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