Abstract
A model of inductive inquiry is defined within a first-order context. Intuitively, the model pictures inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players along with a partition of a class of structures for that vocabulary. Next, Nature secretly chooses one structure (“the real world”) from some cell of the partition. She then presents the scientist with a sequence of atomic facts about the chosen structure. With each new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his inquiry, the scientist's successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. A special kind of scientist selects his hypotheses on the basis of a belief revision operator. We show that reliance on belief revision allows scientists to solve a wide class of problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Cohen, L. J., An Essay on Belief and Acceptance, Oxford University Press, Oxford, UK, 1992.
Earman, J., Bayes or Bust? MIT Press, Cambridge, MA, 1992.
Ebbinghaus, H. D., Flum, J. and Thomas, W., Mathematical Logic, 2nd edn, Springer-Verlag, Berlin, 1994.
Gärdenfors, P., Knowledge in Flux: Modeling the Dynamics of Epistemic States, MIT Press, Cambridge, MA, 1988.
Gärdenfors, P. (ed.), Belief Revision, Cambridge University Press, New York, 1992.
Hansson, S. O., Kernel contraction, J. Symbolic Logic 59(3) (1994), 845-859.
Hansson, S.O., A Textbook of Belief Dynamics: Theory Change and Database Updating, Kluwer Academic Publishers, Norwell, MA, 1999.
Jain, S., Osherson, D., Royer, J. and Sharma, A., Systems that Learn, 2nd edn, MIT Press, Cambridge, MA, 1999.
Keisler, H. J., Fundamentals of model theory, in J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 47-104.
Kelly, K. T., The Logic of Reliable Inquiry, Oxford University Press, New York, NY, 1996.
Kuhn, T. S., The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, Harvard University Press, Cambridge, MA, 1957.
Levi, I., The Enterprise of Knowledge, MIT Press, Cambridge, MA, 1980.
Martin, E. and Osherson, D., Elements of Scientific Inquiry, MIT Press, 1998.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Martin, E., Osherson, D. Scientific Discovery on Positive Data via Belief Revision. Journal of Philosophical Logic 29, 483–506 (2000). https://doi.org/10.1023/A:1026569206678
Issue Date:
DOI: https://doi.org/10.1023/A:1026569206678