The Nature of Nonmonotonic Reasoning
- Charles G. Morgan
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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.
- Besnard, P., and Siegel, P. (1988), ‘The Preferential-models Approach to Nonmonotonic Logics’, in Smets et al., Non-standard Logics for Automated Reasoning, Academic Press, pp. 137–161.
- Besnard, P. (1989), An Introduction to Default Logic. Berlin: Springer-Verlag.
- Brewka, G., Dix, J., and Konolige, K. (1997) Nonmonotonic Reasoning: An Overview. Stanford: Center for the Study of Language and Information.
- Carnap, R. (1962), Logical Foundations of Probability, 2nd ed, Chicago: University of Chicago Press.
- Daniels, C., and Freeman, J. (1980) ‘An Analysis of the Subjunctive Conditional’, Notre Dame Journal of Formal Logic 21, pp. 639–655.
- Delgrande, J. (1988), ‘An Approach to Default Reasoning Based on a First-order Conditional Logic’, Artificial Intelligence 36, pp. 63–90.
- Kraus, S., Lehmann, D., and Magidor, M. (1990), ‘Nonmonotonic Reasoning, Preferential Models and Cumulative Logics’, Artificial Intelligence 44, pp 167–207.
- Kyburg, H. (1994), ‘Believing on the Basis of the Evidence’, Computational Intelligence 10, pp. 3–20.
- Lewis, D. (1973), Counterfactuals, Oxford: Basil Blackwell.
- Morgan, C. and Mares, E. (1991), ‘Conditionals, Probability, and Non-triviality’, Journal of Philosophical Logic 24, pp. 455–467.
- Morgan, C. (1991), ‘Logic, Probability Theory, and Artificial Intelligence-Part 1: the Probabilistic Foundations of Logic’, Computational Intelligence 7, pp. 94–109.
- Morgan, C. (1994), ‘Evidence, Belief, and Inference’, Computational Intelligence 10, pp. 79–84.
- Morgan, C. (1996) ‘Canonical Models and Probabilistic Semantics’, presented at the AnnualMeeting of the Society for Exact Philosophy, held at East Tennessee State University, forthcoming in Logic, Probability and Science, N. Shanks et al., eds., in Poznan Studies in Logic.
- Morgan, C. (1997), ‘Conditionals, Comparative Probability, and Triviality’, presented at the Annual Meeting of the Society for Exact Philosophy, held at McGill University, forthcoming in Topoi.
- Morgan, C. (1998), ‘Non-monotonic Logic is Impossible’, Canadian Artificial Intelligence 42, pp 19–25.
- Poole, D. (1998), ‘A Logical Framework for Default Reasoning’, Artificial Intelligence 36, pp 27–47.
- Reiter, R. (1980), ‘A Logic for Default Reasoning’, Artificial Intelligence 13, pp. 81–132.
- Smets, P. et al., eds. (1988), Non-Standard Logics for Automated Reasoning, London: Academic Press.
- Turner, R. (1984) Logics for Artificial Intelligence, West Sussex: Ellis Horwood Limited.
- Van Fraassen, B. (1981) ‘Probabilistic Semantics Objectified: 1. Postulates and Logics’, Journal of Philosophical Logic 10, pp. 371–394.
- The Nature of Nonmonotonic Reasoning
Minds and Machines
Volume 10, Issue 3 , pp 321-360
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- Kluwer Academic Publishers
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- non-classical logic
- nonmonotonic logic
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- Charles G. Morgan (1) (2)
- Author Affiliations
- 1. Department of Philosophy, University of Victoria, Victoria, B.C, V8W 3P4, Canada
- 2. Varney Bay Institute for Advanced Study, P.O. Box 45, Coal Harbour, B.C. VON 1KO, Canada