Abstract
I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, →, in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, ‘C→B’ holds just in case P[B|C]≥r. Thus, each conditional in a given family behaves like conditional probability above some specific support level.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams, E., 1966: ‘Probability and the Logic of Conditionals’, J. Hintikka and P. Suppes (eds), Aspects of Inductive Logic (North-Holland, Amsterdam), 265–316.
Adams, E., 1975: The Logic of Conditionals (Reidel, Dordrecht).
Field, H., 1977: ‘Logic, Meaning, and Conceptual Role’, Journal of Philosophy 74, 379–409.
Harper, W., 1975: ‘Rational Belicf Change, Popper Functions and Counterfactuals’, Synthese 30, 221–262.
Harper, W., R. Stalnaker, and G. Pearce (eds), 1981: Ifs: Conditionals, Belief, Decision, Chance and Time (Reidel, Dordrecht).
Jackson, F. (ed.), 1991: Conditionals (Oxford Univ. Press, Oxford).
Krantz, D., R. Luce, P. Suppes, and A. Tversky, 1971: Foundations of Measurements, Vol. I (Academic Press, New York).
Kraus, S., D. Lehmann, and M. Magidor, 1990: ‘Nonmonotonic Reasoning, Preferential Models and Cumulative Logics’, Artificial Intelligence 44(1–2), 167–207.
Leblanc, H., 1979: ‘Probabilistic Semantics for First-order Logic’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 25, 497–509.
Leblanc, H., 1983: ‘Alternatives to Standard First-order Semantics’, in D. Gabbay and F. Guenthner (eds), Handbook of Philosophical Logic, Vol. I (Reidel, Dordrecht), Chapter I.3, 189–247.
Lehmann, D. and M. Magidor, 1992: ‘What Does a Conditional Knowledge Base Entail?’ Artificial Intelligence 55, 1–60.
Lewis, D., 1973: Counterfactuals (Harvard Univ. Press, Cambridge, MA).
Narens, L., 1985: Abstract Measure Theory (MIT Press, Cambridge, MA).
Nute, D., 1985: Topics in Conditional Logic (Reigel, Dordrecht).
Nute, D., 1984: ‘Conditional Logic’, in D. Gabbay and F. Guenthner (eds), Handbook of Philosophical Logic, Vol. II (Reidel, Dordrecht), Chapter II.8, 387–439.
Pearl, J., 1988. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Reasoning (Morgan Kaufmann, San Matco, CA).
Pollock, J., 1976: Subjunctive Reasoning (Reidel, Dordrecht).
Popper, K., 1968: The Logic of Scientific Discovery (Harper & Row, New York).
Reinfrank, M., J.De Kleer, M.L. Ginsberg, and E. Sandewall (eds), 1989: Non-Monotonic Reasoning, Lecture Notes in Artificial Intelligence (Springer-Verlag, Berlin).
Savage, L., 1954: The Foundations of Statistics (Wiley, New York; Dover, 1972).
Stalnaker, R., 1968: ‘A Theory of Conditionals’, N. Rescher (ed.), Studies in Logical Theory, American Philosophical Quaterly, Monograph Series 2 (Blackwell, Oxford), 98–112.
Stalnaker, R., 1970: ‘Probability and Conditionals’, Philosophy of Science 37, 64–80.
Suppes, P., D. Krantz, R. Luce, and A. Tversky, 1989: Foundations of Measurement, Vol. II (Academic Press, San Diego).
van Fraassen, B., 1981: ‘Probabilistic Semantics Objectified’, Journal of Philosophical Logic 10, 371–394, 495–510.
Author information
Authors and Affiliations
Additional information
Chris Swoyer provided very helpful comments on drafts of this paper.
Rights and permissions
About this article
Cite this article
Hawthorne, J. On the logic of nonmonotonic conditionals and conditional probabilities. J Philos Logic 25, 185–218 (1996). https://doi.org/10.1007/BF00247003
Issue Date:
DOI: https://doi.org/10.1007/BF00247003