A Logical Approach to Reasoning about Uncertainty: A Tutorial
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.
KeywordsProbability Space Modal Logic Logical Approach Truth Assignment Kripke Structure
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- 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.Google Scholar
- Fagin, R., J. Y. Halpern, Y. Moses, and M. Y. Vardi (1995) Reasoning about Knowledge. MIT Press. Cambridge, Mass.Google Scholar
- Fine, T. L. (1973) Theories of Probability. Academic Press, New York.Google Scholar
- Freund, J. E. (1965) Puzzle or paradox? American Statistician. 19(4):29–44.Google Scholar
- 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.Google Scholar
- Friedman, N. and J. Y. Halpern (1995a) Modeling belief in dynamic systems. Part I: foundations. TechnicalGoogle Scholar
- 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.Google Scholar
- 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”.CrossRefGoogle Scholar
- Hintikka, J. (1962) Knowledge and Belief Cornell University Press, Ithaca, N.Y.Google Scholar
- Hughes, G. E. and M. J. Cresswell (1968) An Introduction to Modal Logic. Methuen, London.Google Scholar
- 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.Google Scholar
- Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Francisco, Calif.Google Scholar
- vos Savant, M. (1991) Ask Marilyn. Parade Magazine, Sept. 9. 1990; Dec. 2, 1990; Feb. 17, 1991.Google Scholar
- Shafer, G. (1976) A Mathematical Theory of Evidence. Princeton University Press, Princeton, N.J.Google Scholar
- 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.Google Scholar