Abstract
We point out a simple but hitherto ignored link between the theoryof updates, the theory of counterfactuals, and classical modal logic: update is a classicalexistential modality, counterfactual is a classical universalmodality, and the accessibility relations corresponding to these modalities are inverses. The Ramsey Rule (often thought esoteric) is simply an axiomatisation of this inverse relationship.
We use this fact to translate between rules for updates andrules for counterfactuals. Thus, Katsuno and Mendelzon‘s postulatesU1--U8 are translated into counterfactual rules C1--C8(Table VII), and many of the familiar counterfactual rulesare translated into rules for updates (Table VIII). Ourconclusions are summarised in Table V.
From known properties of inverse modalities we deduce that notall rules for updates may be translatedinto rules for counterfactuals, and vice versa. We present asyntactic condition which is sufficient to guarantee that atranslation from update to counterfactual (or vice versa) is possible.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bell, J., 1989, "The logic of nonmonotonicity," Artificial Intelligence 41, 365–374.
Burgess, J.P., 1981, "Quick completeness proofs for some logics of conditionals," NotreDame Journal of Formal Logic 22, 76–84.
Chellas, B.F., 1980, "Basic conditional logic," Journal of Philosophical Logic 4, 133–153.
de Rijke, M., 1994, "Meeting some neighbors," in Logic and Information Flow, J. van Eijck and A. Visser, eds., Cambridge, MA: MIT Press.
Gärdenfors, P., 1978, "Conditionals and changes of belief," Acta Philos. Fennica 30, 381–404.
Gärdenfors, P., 1986, "Belief revision and the Ramsey test for conditionals," Philosophical Review 91, 81–93.
Gärdenfors, P., 1988, Knowledge in Flux: Modeling the Dynamics of Epistemic States, Cambridge, MA: MIT Press, Bradford Books.
Goldblatt, R., 1987, Logics of Time and Computation, CSLI Lecture Notes.
Grahne, G., 1991, "Updates and counterfactuals," pp. 269–276 in Proceedings Second International Conference on Principles of Knowledge Representation and Reasoning (KR ’91), n Francisco, CA: Morgan Kaufmann.
Katsuno, H. and Mendelzon, A.O., 1991, "Propositional knowledge base revision and minimal change," Artificial Intelligence 52, 263–294.
Katsuno, H. and Mendelzon, A.O., 1992, "On the difference between updating a knowledge base and revising it," pp. 183–203 in Belief Revision, Volume 29 in Cambridge Tracts in Theoretical Computer Science, P. Gärdenfors, ed., Cambridge: Cambridge University Press.
Keller, A.M. and Winslett Wilkins, M., 1985, "On the use of an extended relational model to handle changing incomplete information," IEEE Transactions on Software Engineering 11(7), 620–633.
Lewis, D.K., 1973, Counterfactuals, Oxford: Basil Blackwell.
Makinson, D., 1985, "How to give it up: A survey of some formal aspects of the logic of theory change," Synthèse 62, 347–363.
Nute, D., 1980, Topics in Conditional Logic, Dordrecht: D. Reidel.
Nute, D., 1984, "Conditional logic," pp. 387–439 in Handbook of Philosophical Logic, Chapter II.8, D.M. Gabbay and F. Guenthner, eds., Dordrecht: D. Reidel.
Pollock, J.L., 1981, "A refined theory of counterfactuals," Journal of Philosophical Logic 10, 239–266.
Popkorn, S., 1994, First Steps in Modal Logic, Cambridge: Cambridge University Press.
Ramsey, F.P., 1931, "Truth and probability," in The Foundations of Probability and Other Logical Essays, R.B. Braithwaite, ed., New York: Harcourt Brace.
Ryan, M. and Schobbens, P.-Y., 1996, "Intertranslating counterfactuals and updates," pp. 100–104 in 12th European Conference on Artificial Intelligence (ECAI), W. Wahlster, ed., Chichester, U.K.: John Wiley & Sons.
Ryan, M., Schobbens, P.-Y., and Rodrigues, O., 1996, "Counterfactuals and updates as inverse modalities," pp. 163–173 in TARK’96: Proceedings Theoretical Aspects of Rationality and Knowledge, Y. Shoham, ed., San Francisco: Morgan Kaufmann.
Stalnaker, R.C., 1968, A Theory of Conditionals, Volume 2 of American Philosophical Quarterly Monograph Series (ed. Nicholas Rescher), pp. 98–112, Oxford: Blackwell.
van Benthem, J., 1984, "Correspondence theory," pp. 167–247 in Handbook of Philosophical Logic, Volume 2, D. Gabbay and F. Guenthner, eds., Dordrecht: D. Reidel.
van Benthem, J., 1991, "Logic and the flow of information," in Proceedings 9th LMPS.
Venema, Y., 1991, "Many-dimensional modal logic," Ph.D. Thesis, Universiteit van Amsterdam.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ryan, M., Schobbens, PY. Counterfactuals and Updates as Inverse Modalities. Journal of Logic, Language and Information 6, 123–146 (1997). https://doi.org/10.1023/A:1008218502162
Issue Date:
DOI: https://doi.org/10.1023/A:1008218502162