Knowledge Representation and Defeasible Reasoning pp 387-403 | Cite as

# A New Normative Theory of Probabilistic Logic

Chapter

## Abstract

Every rational decision-making procedure is founded on some theory of probabilistic logic (also called a theory of rational belief). This article proposes practical and logically correct theories of rational belief that are more general than the probability theory we learn in school, yet remain capable of many of the inferences of this latter theory. We also show why recent attempts to devise novel theories of rational belief usually end up being either incorrect or reincarnations of the more familiar theories we learned in school.

## Keywords

Probabilistic Logic Probability Assignment Belief Function Rational Belief Finite Additivity
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## Bibliography

- Aczel, J.
*Lectures on Functional Equations and Their Applications*, New York, Academic Press, 1966.MATHGoogle Scholar - Buchanan, B. and E. Shortliffe, eds.
*Rule-Based Expert Systems: The MYCIN Experiments of The Stanford Heuristic Programming Project*, Addison-Wesley, 1984.Google Scholar - Burris, S. and H. Sankappanavar.
*A Course in Universal Algebra*, New York, Springer-Verlag, 1981.MATHGoogle Scholar - Carnap, R.
*Logical Foundations of Probability*, University of Chicago Press, 1950.MATHGoogle Scholar - Carnap, R. “The aim of inductive logic,”
*Logic, Methodology, and Philosophy of Science*, E. Nagel, P. Suppes, and A. Tarski, eds., Stanford, Stanford University Press, pp. 303–318, 1962.Google Scholar - Cox, R. “Probability, frequency, and reasonable expectation,”
*American Journal of Physics**14*, pp. 1–13, 1946.MATHCrossRefMathSciNetGoogle Scholar - Cox, R.
*The Algebra of Probable Inference*, Johns Hopkins Press, 1961.MATHGoogle Scholar - Fine, F.
*Theories of Probability: An Examination of Foundations*, Academic Press, 1973.MATHGoogle Scholar - French, S. “Fuzzy decision analysis: some criticisms,”
*Studies in The Management Sciences: Fuzzy Sets and Decision Analysis**20*, Elsevier, 1984.Google Scholar - Fuchs, L.
*Partially Ordered Algebraic Systems*, Pergamon Press, 1963.MATHGoogle Scholar - Good, I.
*Good Thinking, The Foundations of Probability and Its Applications*, University of Minnesota, 1983.MATHGoogle Scholar - Gupta, M., Ragade, R., and R. Yager., eds.
*Advances in Fuzzy Set Theory*, Elsevier, 1979.MATHGoogle Scholar - Heckerman, D. “Probabilistic interpretation for MYCIN’s certainty factors,”
*Uncertainty in Artificial Intelligence*, L. Kanal and J. Lemmer, eds., Elsevier, pp. 167–196, 1986.Google Scholar - Keynes, J.
*Treatise on Probability*, Macmillan, 1921.MATHGoogle Scholar - Koopman, B. “The axioms and algebra of intuitive probability,”
*Annals of Mathematics**42*, 2, pp. 269–292, 1940.CrossRefMathSciNetGoogle Scholar - Koopman, B. “Intuitive probabilities and sequences,”
*Annals of Math-emetics**42*, 1, pp. 169–187, 1941.CrossRefMathSciNetGoogle Scholar - Kyburg, H. “Bayesian and non-Bayesian evidential updating,”
*Artificial Intelligence**31*, 3, pp. 271–293, 1987.MATHCrossRefMathSciNetGoogle Scholar - Kripke, S.
*Naming and Necessity*, Harvard University Press, p. 16, 1980.Google Scholar - McDermott, D., and J. Doyle. “Non-monotonic logic I,”
*Artificial Intelligence**13*, pp. 27–39, 1980.CrossRefMathSciNetGoogle Scholar - McDermott, D. “Non-monotonic logic II: non-monotonic modal theories,”
*Journal of the ACM**21*, 1, pp. 33–57, 1982.CrossRefMathSciNetGoogle Scholar - Morgan, C. “There is a probabilistic semantics for every extension of classical sentence logic,”
*Journal of Philosophical Logic**11*, pp. 431–442, 1982.MATHMathSciNetGoogle Scholar - Poole, D., Goebel, R., and R. Aleliunas. “Theorist: a logical reasoning system for defaults and diagnosis,”
*Knowledge Frontier*, N. Cerone, and G. McCalla, eds., Spring-Verlag, pp. 331–352, 1987.CrossRefGoogle Scholar - Reiter, R. “A logic for default reasoning,”
*Artificial Intelligence**13*, pp. 81–132, 1980.MATHCrossRefMathSciNetGoogle Scholar - Zadeh, L. “Fuzzy sets,”
*Information and Control**8*, pp. 338–353, 1965.MATHCrossRefMathSciNetGoogle Scholar

## Copyright information

© Kluwer Academic Publishers 1990