Minds and Machines

, Volume 10, Issue 3, pp 321–360 | Cite as

The Nature of Nonmonotonic Reasoning

  • Charles G. Morgan


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.

logic non-classical logic nonmonotonic logic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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.Google Scholar
  2. Besnard, P. (1989), An Introduction to Default Logic. Berlin: Springer-Verlag.Google Scholar
  3. Brewka, G., Dix, J., and Konolige, K. (1997) Nonmonotonic Reasoning: An Overview. Stanford: Center for the Study of Language and Information.Google Scholar
  4. Carnap, R. (1962), Logical Foundations of Probability, 2nd ed, Chicago: University of Chicago Press.Google Scholar
  5. Daniels, C., and Freeman, J. (1980) ‘An Analysis of the Subjunctive Conditional’, Notre Dame Journal of Formal Logic 21, pp. 639–655.Google Scholar
  6. Delgrande, J. (1988), ‘An Approach to Default Reasoning Based on a First-order Conditional Logic’, Artificial Intelligence 36, pp. 63–90.Google Scholar
  7. Kraus, S., Lehmann, D., and Magidor, M. (1990), ‘Nonmonotonic Reasoning, Preferential Models and Cumulative Logics’, Artificial Intelligence 44, pp 167–207.Google Scholar
  8. Kyburg, H. (1994), ‘Believing on the Basis of the Evidence’, Computational Intelligence 10, pp. 3–20.Google Scholar
  9. Lewis, D. (1973), Counterfactuals, Oxford: Basil Blackwell.Google Scholar
  10. Morgan, C. and Mares, E. (1991), ‘Conditionals, Probability, and Non-triviality’, Journal of Philosophical Logic 24, pp. 455–467.Google Scholar
  11. Morgan, C. (1991), ‘Logic, Probability Theory, and Artificial Intelligence-Part 1: the Probabilistic Foundations of Logic’, Computational Intelligence 7, pp. 94–109.Google Scholar
  12. Morgan, C. (1994), ‘Evidence, Belief, and Inference’, Computational Intelligence 10, pp. 79–84.Google Scholar
  13. 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.Google Scholar
  14. 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.Google Scholar
  15. Morgan, C. (1998), ‘Non-monotonic Logic is Impossible’, Canadian Artificial Intelligence 42, pp 19–25.Google Scholar
  16. Poole, D. (1998), ‘A Logical Framework for Default Reasoning’, Artificial Intelligence 36, pp 27–47.Google Scholar
  17. Reiter, R. (1980), ‘A Logic for Default Reasoning’, Artificial Intelligence 13, pp. 81–132.Google Scholar
  18. Smets, P. et al., eds. (1988), Non-Standard Logics for Automated Reasoning, London: Academic Press.Google Scholar
  19. Turner, R. (1984) Logics for Artificial Intelligence, West Sussex: Ellis Horwood Limited.Google Scholar
  20. Van Fraassen, B. (1981) ‘Probabilistic Semantics Objectified: 1. Postulates and Logics’, Journal of Philosophical Logic 10, pp. 371–394.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Charles G. Morgan
    • 1
    • 2
  1. 1.Department of PhilosophyUniversity of VictoriaVictoriaCanada
  2. 2.Varney Bay Institute for Advanced StudyCoal HarbourCanada

Personalised recommendations