Automatic derivation of probabilistic inference rules

International Journal of Approximate Reasoning

Volumn 28, Issue 1, 2001, Pages 1-22

  Jaeger, Manfred ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

Conditional probabilities; Inference rules; Probabilistic logic; Symbolic computation

Indexed keywords

CONSTRAINT THEORY;

CONDITIONAL PROBABILITIES; PROBABILISTIC INFERENCE RULES; SYMBOLIC COMPUTATION;

PROBABILISTIC LOGICS;

EID: 1842860809     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0888-613X(01)00044-5     Document Type: Article

References (20)

1. S. Amarger, D. Dubois, H. Prade, Constraint propagation with imprecise conditional probabilities, in: Proceedings of the Seventh Annual Conference on Uncertainty in Artificial Intelligence (UAI-91), Morgan Kaufmann, San Mateo, CA 1991, pp. 26-34.
2. G. Boole, Investigations of Laws of Thought on which are Founded the Mathematical Theories of Logic and Probabilities, London, 1854.
3. G. Boole, On the theory of probabilities, Phil. Trans. R. Soc. London 152 (1862).
4. D. Dubois, H. Prade, J.-M. Toucas, Inference with imprecise numerical quantifiers, in: Z. Ras, M. Zemankova (Eds.), Intelligent Systems: State of the Art and Future Directions, Ellis Horwood, Chichester, UK, 1990, pp. 52-72.
5. R. Fagin, J.Y. Halpern, N. Megiddo, A logic for reasoning about probabilities, Information and Computation 87 (1990) 78-128.
6. A.M. Frisch, P. Haddawy, Anytime deduction for probabilistic logic, Artificial Intelligence 69 (1994) 93-122.
7. K.O. Geddes, S.R. Czapor, G. Labahn, Algorithms for Computer Algebra, Kluwer Academic Publishers, Dordrecht, 1992.
8. D. Geiger, C. Meek, Quantifier elimination for statistical problems, in: Proceedings of the Fifteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-99), Morgan Kaufmann, San Francisco, CA, 1999, pp. 226-235.
9. T. Hailperin, Best possible inequalities for the probability of a logical function of events, American Mathematical Monthly 72 (1965) 343-359.
10. T. Hailperin, Boole's Logic and Probability, volume 85 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1976.
11. T. Hailperin, Sentential Probability Logic, Lehigh University Press, Bethlehem, 1996.
12. J. Heinsohn. Probabilistic description logics, in: Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-94), Seattle, WA, 1994, pp. 311-318.
13. C. Luao, C. Yu, J. Lobo, G. Wang, T. Pham, Computation of best bounds of probabilities from uncertain data, Computational Intelligence 12 (4) (1996) 541-566.
14. T. Lukasiewicz, Local probabilistic deduction from taxonomic and probabilistic knowledge-bases over conjunctive events, International Journal of Approximate Reasoning 21 (1999) 23-61.
15. N. Nilsson, Probabilistic logic, Artificial Intelligence 28 (1986) 71-88.
16. G. Paaß, Probabilistic logic, in: D. Dubois, P. Smets, A. Mamdani, H. Prade (Eds.), Non-Standard Logics for Automated Reasoning, Academic Press, New York, 1988, pp. 213-251 (Chapter 8).
17. J. Renegar, On the computational complexity and geometry of the first-order theory of the reals, parts i-iii, Journal of Symbolic Computation 13 (1992) 255-352.
18. A. Schrijver, Theory of Linear and Integer Programming, Wiley, New York, 1986.
19. A. Tarski, A Decision Method for Elementary Algebra and Geometry, University of California Press, Berkeley, CA, 1951.
20. H. Thöne, U. Güntzer, W. Kießling, Towards precision of probabilistic bounds propagation, in: Proceedings of the Eighth Annual Conference on Uncertainty in Artificial Intelligence (UAI-92), Morgan Kaufmann, San Francisco, CA, 1992, pp. 315-322.