Conclusion
Using probability functions defined over a simple language as models of states of belief, my goal in this article has been to analyse contractions and revisions of beliefs. My first strategy was to formulate postulates for these processes. Close parallels between the postulates for contractions and the postulates for revisions have been established - the results in Section 5 show that contractions and revisions are interchangeable.
As a second strategy, some suggestions for more or less explicit constructive definitions of the revision process (and indirectly also of the contraction process) were then presented. However, the results in Section 6 are less conclusive than in the earlier ones. This problem area still awaits further development.
Similar content being viewed by others
References
Alchourrón, C. E., P. Gärdenfors, and D. Makinson: 1985, ‘On the logic of theory change: Partial meet contraction and revision functions’, Journal of Symbolic Logic 50, 510–530.
Domotor, Z.: 1983, The Structure of Probabilistic Knowledge, manuscript, Department of Philosophy, University of Pennsylvania.
Gärdenfors, P.: 1978, ‘Conditionals and changes of belief, in I. Niiniluoto and R. Tuomela (eds.), The Logic and Epistemology of Scientific Change (Acta Philosophica Fennica 30, issues 2–4), North-Holland, Amsterdam.
Gärdenfors, P.: 1982a, ‘Rules for rational changes of belief’, in T. Pauli (ed.), 〈320311〉: Philosophical Essays Dedicated to Lennart Åqvist on his Fiftieth Birthday, Department of Philosophy, Uppsala.
Gärdenfors, P.: 1982b, ‘Imaging and conditionalization’, Journal of Philosophy 79, 747–760.
Gärdenfors, P.: 1984, ‘Epistemic importance and minimal changes of belief’, Australasian Journal of Philosophy 62, 136–157.
Harper, W. L.: 1976, ‘Rational belief change, Popper functions and counterfactuals’, in W. L. Harper and C. H. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. I, Reidel, Dordrecht.
Levi, I.: 1977, ‘Subjunctives, dispositions and chances’, Synthese 34, 423–455.
Lewis, D.: 1976, ‘Probabilities of conditionals and conditional probabilities’, Philosophical Review 85, 297–315.
Makinson, D.: 1985, ‘How to give it up: A survey of some formal aspects of the logic of theory change’, Synthese 62, 347–363.
Popper, K. R.: 1959, The Logic of Scientific Discovery, Hutchinson, London.
Stalnaker, R.: 1970, ‘Probability and conditionals’, Philosophy of Science 37, 64–80.
Teller, P.: 1976, ‘Conditionalization, observation and change of preference’, in W. L. Harper and C. H. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. I, Reidel, Dordrecht.
van Fraassen, B.: 1976, ‘Representation of conditional probabilities’, Journal of Philosophical Logic 5, 417–430.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gärdenfors, P. The dynamics of belief: Contractions and revisions of probability functions. Topoi 5, 29–37 (1986). https://doi.org/10.1007/BF00137827
Issue Date:
DOI: https://doi.org/10.1007/BF00137827