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Proof systems for probabilistic uncertain reasoning

Published online by Cambridge University Press:  12 March 2014

J. Paris  and
A. Vencovská
J. Paris
Affiliation:
Department of Mathematics, Manchester University, Manchester, M13 9PL, UK E-mail: [email protected]
A. Vencovská
Affiliation:
Department of Mathematics, Manchester University, Manchester, M13 9PL, UK E-mail: [email protected]
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Abstract

The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 3 , September 1998 , pp. 1007 - 1039
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1]Fagin, R., Halpern, J., and Megiddo, N., A logic for reasoning about probabilities, Proceedings of the 3rd IEEE symposium on logic in computer science, 1988, pp. 277–291.Google Scholar
[2]Gabbay, D., Theoretical foundations for non-monotonic reasoning in expert systems, Proceedings of the NATO advanced study institute on logic and concurrent systems (Apt, K., editor), Springer-Verlag, Berlin, 1985, pp. 439–457.Google Scholar
[3]Hajek, P., Havranek, T., and Jirousek, R., Uncertain information processing in expert systems, 1992.Google Scholar
[4]Kemeny, J. G. and Snell, J. L., Finite Markov chains, D. Van Nostrand Co., 1959.Google Scholar
[5]Kraus, S., Lehmann, D., and Magidor, M., Non-monotonic reasoning, preferential models and cummulative logics, Artificial Intelligence, vol. 44 (1990), pp. 167–202.CrossRefGoogle Scholar
[6]Lauritzen, S. L. and Spiegelhalter, D. J., Local computations with probabilities on graphical structures and their applications to expert systems, Journal of the Royal Statistical Society B, vol. 50 (1988), no. 2, pp. 157–224.Google Scholar
[7]Lehmann, D. and Magidor, M., What does a conditional knowledge base entail?, Proceedings of the first international conference on principles of knowledge representation and reasoning (Brachman, R. and Levesque, H. J., editors), 1989.Google Scholar
[8]Lehner, P., Probabilities and reasoning about probabilities, International Journal of Approximate Reasoning, vol. 5 (1991), no. 1, pp. 27–43.CrossRefGoogle Scholar
[9]Makinson, D., General theory of cummulative inference, Proceedings of the second international workshop on non-monotonic reasoning (Reinfrank, M.et al., editors), Lecture Notes in Artificial Intelligence, no. 346, 1988, pp. 1–18.Google Scholar
[10]Maung, I., Ph.D. thesis, University of Manchester, 1992.Google Scholar
[11]Nilson, N., Probabilistic logic, Artificial Intelligence, vol. 28 (1986), pp. 71–87.CrossRefGoogle Scholar
[12]Paris, J., The uncertain reasoner's companion, Cambridge Tracts in Theoretical Computer Science, no. 39, Cambridge University Press, 1994.Google Scholar
[13]Paris, J. and Vencovská, A., Inexact and inductive reasoning, Logic, methodology and philosophy of science (Fenstadt, J. E.et al., editors), vol. VIII, Elsevier Science Publishers B.V., 1988, pp. 111–120.Google Scholar
[14]Paris, J. and Vencovská, A., Maximum entropy and inductive inference, Maximum entropy and Bayesian methods (Skilling, J., editor), Kluwer Academic Publishers, 1989, pp. 397–403.CrossRefGoogle Scholar
[15]Paris, J. and Vencovská, A., A note on the inevitability of maximum entropy, International Journal of Approximate Reasoning, vol. 4 (1990), no. 3, pp. 183–224.CrossRefGoogle Scholar
[16]Paris, J. and Vencovská, A., A method of updating justifying minimum cross entropy, International Journal of Approximate Reasoning, vol. 7 (1992), no. 1, pp. 1–18.CrossRefGoogle Scholar
[17]Paris, J. and Vencovská, A., Principles of uncertain reasoning, Philosophy and cognitive science (Clark, A.et al., editors), Kluwer Academic Publishers, 1996, pp. 221–259.Google Scholar
[18]Pearl, J., Probabilistic reasoning in intelligent systems, Morgan Kaufmann, 1988.Google Scholar
[19]Pulley, C., Ph.D. thesis, University of Manchester, 1991.Google Scholar
[20]Rhodes, P. C. and Garside, G. R., Computing marginal probabilities in causal inverted binary trees given incomplete information, to appear in Knowledge Based Systems.Google Scholar
[21]Shafer, G., A mathematical theory of evidence, Princeton University Press, 1976.CrossRefGoogle Scholar
[22]Simon, H. A., Information processing theories of human problem solving, Handbook of learning and cognitive processes (Estes, W. K., editor), Erlbaum, Hillsdale, NJ, 1978.Google Scholar
[23]Vervoort, M., University of Amsterdam, private communication, 1996.Google Scholar
[24]Voorbraak, F., Probabilistic belief expansion and conditioning, submitted to the Journal of Logic, Language and Information.Google Scholar
[25]Walley, P., Statistical reasoning with imprecise probabilities, Chapman and Hall, London, 1991.CrossRefGoogle Scholar
[26]Wilson, R., Introduction to graph theory, Oliver and Boyd, Edinburgh, 1972.Google Scholar