Skip to main content
Log in

Iterated Belief Revision, Reliability, and Inductive Amnesia

  • Published:
Erkenntnis Aims and scope Submit manuscript

Abstract

Belief revision theory concerns methods for reformulating an agent's epistemic state when the agent's beliefs are refuted by new information. The usual guiding principle in the design of such methods is to preserve as much of the agent's epistemic state as possible when the state is revised. Learning theoretic research focuses, instead, on a learning method's reliability or ability to converge to true, informative beliefs over a wide range of possible environments. This paper bridges the two perspectives by assessing the reliability of several proposed belief revision operators. Stringent conceptions of “minimal change” are shown to occasion a limitation called inductive amnesia: they can predict the future only if they cannot remember the past. Avoidance of inductive amnesia can therefore function as a plausible and hitherto unrecognized constraint on the design of belief revision operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Arlo-Costa, H.: In press, ‘Belief Revision Conditionals: Basic Iterated Systems’, Annals of Pure and Applied Logic.

  • Boutilier, C.: 1993, ‘Revision Sequences and Nested Conditionals’, in Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning, pp. 519-25.

  • Darwiche, A. and J. Pearl: 1997, ‘On the Logic of Iterated Belief Revision’, 89, 1-29.

    Google Scholar 

  • Earman, J.: 1992, Bayes or Bust, MIT Press, Cambridge.

    Google Scholar 

  • Gärdenfors, P.: 1988 Knowledge in Flux, MIT Press, Cambridge.

    Google Scholar 

  • Glaister, S. M.: 1997, ‘Symmetry and Belief Revision’, unpublished manuscript.

  • Gold, E. M.: 1967 ‘Language Identification in the Limit’, Information and Control 10, 302-20.

    Google Scholar 

  • Goldszmidt, M. and J. Pearl: 1994, ‘Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling’, Technical Report r-161-L, Revision II.

  • Goodman, N.: 1983, Fact, Fiction and Forecast, 4th edn. Harvard University Press, Cambridge.

    Google Scholar 

  • Grove, A.: 1988, ‘Two Modellings for Theory Change’, Journal of Philosohical Logic 17, 157-70.

    Google Scholar 

  • James, W.: 1948, ‘The Will to Believe’, in A. Castell (ed), Essays in Pragmatism, Macmillan, New York.

    Google Scholar 

  • Katsuno, H. and A. O. Mendelzon: 1991, ‘Propositional Knowledge Base Revision and Minimal Change’, Journal of Artificial Intelligence 52, 263-94.

    Google Scholar 

  • Kelly, K. T.: 1996, The Logic of Reliable Inquiry, Oxford University Press, New York.

    Google Scholar 

  • Kelly, K. T. and O. Schulte: 1995, ‘The Computable Testability of Theories Making Uncomputable Predictions’, Erkenntnis 43, 29-66.

    Google Scholar 

  • Kelly, K. T., O. Schulte, and V. Hendricks: 1997, ‘Reliable Belief Revision’, in Maria Luisa Dalla Chiara (ed.), Proceedings of the 10th International Congress of Logic, Methodology, and Philosophy of Science, Kluwer, Dordrecht.

    Google Scholar 

  • Kemeny, J.: 1953, ‘The Use of Simplicity in Induction’, Philosophical Review 62, 391-408.

    Google Scholar 

  • Kuhn, T.: 1970, The Structure of Scientific Revolutions, University of Chicago Press, Chicago.

    Google Scholar 

  • Levi, I.: 1996, The Enterprise of Knowledge, MIT Press, Cambridge.

    Google Scholar 

  • Levi, I.: 1996, For the Sake of the Argument: Ramsey Test Conditionals, Inductive Inference, and Nonmonotonic Reasoning, Cambridge University Press, Cambridge.

    Google Scholar 

  • Martin, E. and D. Osherson: 1997, ‘Scientific Discovery via Rational Hypothesis Revision’, in Maria Luisa Dalla Chiara (ed.), Proceedings of the 10th International Congress of Logic, Methodology, and Philosophy of Science, Kluwer, Dordrecht.

    Google Scholar 

  • Martin, E. and D. Osherson: In press, ‘Scientific Discovery Based on Belief Revision’, Journal of Symbolic Logic.

  • Martin, E. and D. Osherson: 1998, Elements of Scientific Inquiry, MIT Press, Cambridge.

    Google Scholar 

  • Nayak, A. C.: 1994, ‘Iterated Belief Change Based on Epistemic Entrenchment’, Erkenntnis 41, 353-90.

    Google Scholar 

  • Oshersion, D., M. Stob, and S. Weinstein: 1986, Systems that Learn, MIT Press, Cambridge.

    Google Scholar 

  • Popper, K.R.: 1968, The Logic of Scientific Discovery, Harper, New York.

    Google Scholar 

  • Putnam, H.: 1963, ‘“Degree of Confirmation” and Inductive Logic’, in A. Schilpp (ed.), The Philosophy of Rudolph Carnap, Open Court, LaSalle, IL.

    Google Scholar 

  • Ramsey, F.P.: 1990, in H. A. Mellor (ed.), Philosophical Papers, Cambridge University Press, Cambridge.

    Google Scholar 

  • Samet, D.: 1996, ‘Hypothetical Knowledge and Games with Perfect Information’, Games and Economic Behavior 17, 230-51.

    Google Scholar 

  • Spohn, W.: 1988, ‘Ordinal Conditional Functions: A Dynamic Theory of Epistemic States’, Causation in Decision, Belief Change, and Statistics, II, in B. Skyrms and W. L. Harper, (eds.), Kluwer, Dordrecht.

    Google Scholar 

  • Spohn, W.: 1990, ‘A General Non-probabilisistic Theory of Inductive Reasoning’, Uncertainty in Artificial Intelligence 4, 149-59.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kelly, K.T. Iterated Belief Revision, Reliability, and Inductive Amnesia. Erkenntnis 50, 7–53 (1999). https://doi.org/10.1023/A:1005444112348

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005444112348

Keywords

Navigation