Abstract
Uncertainty is a fundamental—and unavoidable—feature of daily life. In order to deal with uncertainty intelligently, we need to be able to represent it and reason about it. These notes describe a systematic approach for doing so. I have made no attempt to be comprehensive here; I have been guided by my biases and my own research.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bar-Hillel, M. and R. Falk (1982) Some teasers concerning conditional probabilities. Cognition 11:109–122.
Dubois, D. and H. Prade (1990) An introduction to possibilistic and fuzzy logics. In G. Shafer and J. Pearl, editors. Readings in Uncertain Reasoning. Morgan Kaufmann. San Francisco, Calif.
Fagin, R. and J. Y. Halpern (1994) Reasoning about knowledge and probability. Journal of the ACM 41(2):340–367.
Fagin, R., J. Y. Halpern, and N. Megiddo (1990) A logic for reasoning about probabilities. Information and Computation, 87(1/2):78–128.
Fagin, R., J. Y. Halpern, Y. Moses, and M. Y. Vardi (1995) Reasoning about Knowledge. MIT Press. Cambridge, Mass.
Fine, T. L. (1973) Theories of Probability. Academic Press, New York.
Freund, J. E. (1965) Puzzle or paradox? American Statistician. 19(4):29–44.
Friedman, N. and J. Y. Halpern (1994) A knowledge-based framework for belief change. Part I: foundations. In R. Fagin, editor. Theoretical Aspects of Reasoning about Knowledge: Proc. Fifth Conference, pages 44–64. Morgan Kaufmann. San Francisco, Calif.
Friedman, N. and J. Y. Halpern (1995a) Modeling belief in dynamic systems. Part I: foundations. Technical
Report RJ9965. IBM. Available by anonymous ftp from starry.stanford.edu/pub/nir or via WWW at http://robotics.stanford.edu/users/nir. To appear, Artificial Intelligence.
Friedman, N. and L. Y. Halpern (1995b) Plausibility measures: a user’s manual. In P. Besnard and S. Hanks, editors, Proc. Eleventh Conference on Uncertainty in Artificial Intelligence (UAI ‘95). Morgan Kaufmann, San Francisco, Calif.
Halpern, J. Y. and M. R. Tultle (1993) Knowledge, probability, and adversaries. Journal of the ACM, 40(4):917–962.
Halpern, J. Y. and M. Y. Vardi (1989) The complexity of reasoning about knowledge and time, I: lower bounds. Journal of Computer and System Sciences, 38(1): 195–237.
Halpern, J. Y. and R. Fagin (1989) Modelling knowledge and action in distributed systems. Distributed Computing, 3(4): 159–179. A preliminary version appeared in Proc. 4th ACM Symposium on Principles of Distributed Computing, 1985, with the title “A formal model of knowledge, action, and communication in distributed systems: preliminary report”.
Halpern, J. Y. and Y. Moses (1992) A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54:319–379.
Hintikka, J. (1962) Knowledge and Belief Cornell University Press, Ithaca, N.Y.
Hughes, G. E. and M. J. Cresswell (1968) An Introduction to Modal Logic. Methuen, London.
Kraus, S., D. Lehmann, and M. Magidor (1990) Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence. 44:167–207.
Morgan, J. P., N. R. Chaganty, R. C. Dahiya, and M. J. Doviak (1991) Let’s make a deal: the player’s dilemma (with commentary). The American Statistician, 45(4):284–289.
Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Francisco, Calif.
vos Savant, M. (1991) Ask Marilyn. Parade Magazine, Sept. 9. 1990; Dec. 2, 1990; Feb. 17, 1991.
Shafer, G. (1976) A Mathematical Theory of Evidence. Princeton University Press, Princeton, N.J.
Shafer, G. (1985) Conditional probability. International Statistical Review. 53(3):261–277.
Spohn, W. (1987) Ordinal conditional functions: a dynamic theory of epistemic states. In W. Harper and B. Skyrms, editors, Causation in Decision, Belief Change, and Statistics, volume 2, pages 105–134. Reidel, Dordrecht, Holland.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Halpern, J.Y. (1998). A Logical Approach to Reasoning about Uncertainty: A Tutorial. In: Arrazola, X., Korta, K., Pelletier, F.J. (eds) Discourse, Interaction and Communication. Philosophical Studies Series, vol 72. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8994-9_8
Download citation
DOI: https://doi.org/10.1007/978-94-015-8994-9_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4996-4
Online ISBN: 978-94-015-8994-9
eBook Packages: Springer Book Archive