Abstract
We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a “virtual’ manner, using uniterated revision.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ernest W. Adams, The Logic of Conditionals, D. Reidel Dordrecht, 1975.
Carlos Alchourrón, Peter Gärdenfors, and David Makinson. On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50: 510–530, 1985.
Carlos Alchourón and David Makinson. On the logic of theory change: Safe contraction. Studia Logica, 44(4): 405–422, 1985.
Craig Boutilier. Inaccessible worlds and irrelevance: Preliminary report. In Proceedings of the Twelfth International Joint Conference on Artificial Inteligence, pages 413–418, Sydney, 1991.
Craig, Boutilier. Epistemic entrenchment in autoepistemic logic Fundamenta Informaticae, 17(1–2): 5–30, 1992.
Craig Boutilier Sequences of revisions: On the semantics of nested conditionals. Technical Report 92–24, University of British Columbia, Vancouver, 1992.
Craig Boutilier. The probability of a possibility: Adding uncertainly to default rules. In Proceedings of the Ninth Conference on Uncertainty in Al, pages 461–468. Washington, D.C. 1993.
Craig Boutilier. Conditional logics of normality: A modal approach. Artificial Intelligence, 68: 87–154, 1994.
Craig Boutilier. Unifying default reasoning and belief revision in a modal framework, Artificial Intelligence, 68: 33–85, 1994.
Craig Boutilier and Moisés Goldszmidt. Revision by conditional beliefs. In Proceedings of the Eleventh National Conference on Artificial Intelligence, pages 649–654, Washington, D.C., 1993.
Craig, Boutilier and Moisés Golszmidt. A theory of conditional belief revision. In G. Crocco, L. Fari nas del Cerro, and A. Herzig, editors, Conditional Logics in Artificial Intelligence. Oxford University Press, London, 1995 (to appear).
Adnan Darwiche and Judea Pearl. On the logic of iterated belief revision. In Proceedings of the Fifth Conference on Theoretical Aspects of Reasoning about Knowledge, pages 5–23, Pacific Grove, 1994.
André Fuhrmann. Theory contraction through base contraction. Journal of Philosophical Logic, 20: 175–203, 1991.
Peter Gärdenfors. Belief revisions and the Ramsey test for conditionals. The Philosophical Review, 95: 81–93, 1986.
Peter Gärdenfors, Knowledge in Flux: Modelind the Dynamics of Epistemic States. MIT Press, Cambridge, 1988.
Peter Gärdenfors and David Makinson. Revisions of Knowledge systems using epistemic entrenchment. In Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge, pages 83–95, Pacific Grove, 1988.
Peter Gärdenfors and David Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence, 65: 197–245, 1994.
Moisés Goldszmidt and Judea Pearl. Reasoning with qualitative probabilities can be tractable. In Proceedings of the Eighth Conference on Uncertainty in Al, pages 112–120, Stanford, 1992.
Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17: 157–170, 1988.
Sven Ove Hansson. In defense of base contraction. Synthese, 91: 239–245, 1992.
Sven Ove Hansson. In defense of the Ramsey test. Journal of Philosophy, 89: 522–540, 1992.
Hector J. Levesque. All I know: A study in autoepistemic logic. Artificial Intelligence, 42:263–309, 1990.
Isaac, Levi. Iteration of conditionals and the Ramsey test. Synthese, 76(1):49–81, 1988.
David Lewis. Counterfactuals. Blackwell, Oxford, 1973.
David Makinson and Peter Gärdenfors. Relations between the logic of theory change and nonmonotonic logic. In Andre Fuhrmann and Michael Moreau, editors, The Logic of Theory Change, pages 185–205, Springer-Verlag, Berlin, 1990.
Judea Pearl, System, Z: A natural ordering of defaults with tractable applications to default reasoning. In M. Vardi, editor, Proceedings of Theoretical Aspects of Reasoning about Knowledge, pages 121–135. Morgan Kaufmann, San Mateo, 1990.
Hans Rott. Conditionals and theory change: Revisions, expansions, and additions. Synthese, 81:(1):91–113, 1989.
Hans Rott. A nonmonotonic conditional logic for belief revision. In A. Fuhrmann and M. Morreau, editors, The Logic of Theory Change, pages 135–181. Springer-Verlag, Berlin, 1990.
Hans Rott. Belief change using generalized epistemic entrenchment. Journal of Logic, Language and Information, 1(1):45–78, 1992.
Karl Schlechta. Theory revision and probability. Notre Dame Journal of Formal Logic, 307(2):307–318, 1991.
Wolfgang Spohn. Ordinal conditional functions: A dynamic theory of epistemic states. In W.L. Harper and B. Skyrms, editors, Causation in Decision, Belief Change and Statistics, Volume 2, pages 105–134. D. Reidel, Dordrecht, 1987.
Robert C. Stalnaker. A theory of conditionals. In W.L. Harper, R. Stalnaker, and G. Pearce, editors, Ifs, pages 41–55. D. Reidel, Dordrecht, 1968. 1981.
Robert C. Stalnaker. Inquiry. MIT Press, Cambridge, 1984.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Boutilier, C. Iterated revision and minimal change of conditional beliefs. J Philos Logic 25, 263–305 (1996). https://doi.org/10.1007/BF00248151
Issue Date:
DOI: https://doi.org/10.1007/BF00248151