Minds and Machines 10 (3):321-360 (2000)

Authors
Charles Morgan
University of Pennsylvania
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
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Reprint years 2004
DOI 10.1023/A:1026560718525
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Defeasible Reasoning.Robert C. Koons - 2008 - Stanford Encyclopedia of Philosophy.
A Nonmonotonic Sequent Calculus for Inferentialist Expressivists.Ulf Hlobil - 2016 - In Pavel Arazim & Michal Dančák (eds.), The Logica Yearbook 2015. College Publications. pp. 87-105.
Must Good Reasoning Satisfy Cumulative Transitivity?Shyam Nair - 2019 - Philosophy and Phenomenological Research 98 (1):123-146.
Applied Logic Without Psychologism.Gregory Wheeler - 2008 - Studia Logica 88 (1):137-156.
Whither Consequence?John Woods - 2011 - Informal Logic 31 (4):318-343.

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