Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-23T13:34:45.092Z Has data issue: false hasContentIssue false
  • English
  • Français

A DECISION PROCEDURE FOR PROBABILITY CALCULUS WITH APPLICATIONS

Published online by Cambridge University Press:  01 June 2008

BRANDEN FITELSON
BRANDEN FITELSON*
Affiliation:
University of California – Berkeley
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF CALIFORNIA, BERKELEY, BERKELEY, CA 94720, USA. E-mail: branden@fitelson.org
Get access Rights & Permissions [Opens in a new window]

Abstract

A decision procedure (PrSAT) for classical (Kolmogorov) probability calculus is presented. This decision procedure is based on an existing decision procedure for the theory of real closed fields, which has recently been implemented in Mathematica. A Mathematica implementation of PrSAT is also described, along with several applications to various non-trivial problems in the probability calculus.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 1 , June 2008 , pp. 111 - 125
Copyright
Copyright © Association for Symbolic Logic 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Basu, S., Pollack, R., & Roy, M. F. (1996). On the combinatorial and algebraic complexity of quantifier elimination. Journal of the ACM, 43, 1002–1045.CrossRefGoogle Scholar
Brown, C. (2001a). Improved projection for cylindrical algebraic decomposition. Journal of Symbolic Computation, 32, 447–465.CrossRefGoogle Scholar
Brown, C. (2001b). Simple CAD construction and its applications. Journal of Symbolic Computation, 31, 521–547.CrossRefGoogle Scholar
Caviness, B., & Johnson, J., editors. (1998). Quantifier Elimination and Cylindrical Algebraic Decomposition. Vienna: Springer-Verlag.CrossRefGoogle Scholar
Collins, G. (1975). Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Reprinted in Caviness and Johnson [1998], pp. 85–121.Google Scholar
Davenport, J. H., & Heintz, J. (1988). Real quantifier elimination is doubly exponential. Journal of Symbolic Computation, 5, 29–35.CrossRefGoogle Scholar
Feferman, A. B., & Feferman, S. (2004). Alfred Tarski: Life and Logic. Cambridge: Cambridge University Press.Google Scholar
Feller, W. (1968). An Introduction to Probability Theory and Its Applications (third edition), vol. 1. New York: John Wiley & Sons Inc.Google Scholar
Fitelson, B. (1999). The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science, 66, S362–S378. Available online from: http://fitelson.org/psa.pdf.CrossRefGoogle Scholar
Fitelson, B. (2001a). A Bayesian account of independent evidence with applications. Philosophy of Science, 68, S123–S140. Available online from: http://fitelson.org/psa2.pdf.CrossRefGoogle Scholar
Fitelson, B. (2001b). Studies in Bayesian confirmation theory. PhD Thesis, University of Wisconsin – Madison (Philosophy). Available online from: http://fitelson.org/thesis.pdf.Google Scholar
Fitelson, B., & Hawthorne, J. (to appear). How Bayesian confirmation theory handles the paradox of the ravens. In Eells, E., & Fetzer, J., editors, Probability in Science. Open Court. Available online from: http://fitelson.org/ravens.pdf.Google Scholar
Hong, H. (1990). An improvement of the projection operator in cylindrical algebraic decomposition. Reprinted in Caviness and Johnson [1998], pp. 166–173.CrossRefGoogle Scholar
Hong, H. (1991). Comparison of Several Decision Algorithms for the Existential Theory of the Reals. Technical Report 91–41, Johannes Kepler University, Linz, Austria. Available online from: http://citeseer.ist.psu.edu/hong91comparison.html.Google Scholar
Hong, H. (1992). Simple solution formula construction in cylindrical algebraic decomposition based quantifier elimination. In Wang, P., editor (1992). ISSAC ’92: Papers from the International Symposium on Symbolic and Algebraic Computation. New York: Association for Computing Machinery, pp. 177–188.CrossRefGoogle Scholar
Hong, H. (2006). QEPCAD – Quantifier elimination by partial cylindrical algebraic decomposition. Computer Program Web site. Available online from: http://www.cs.usna.edu/qepcad/.Google Scholar
Huntington, G. (to appear). Decision procedures for the pure existential fragment of the theory of real-closed fields. PhD Dissertation, Group in Logic and the Methodology of Science, UC – Berkeley.Google Scholar
Joyce, J. (2003). Bayes's Theorem. The Stanford Encyclopedia of Philosophy. Available online from: http://plato.stanford.edu/entries/bayes-theorem/.Google Scholar
Kolmogorov, A. (1956). Foundations of Probability (second edition). New York: AMS Chelsea.Google Scholar
McCallum, S. (1998). An improved projection operator for cylindrical algebraic decomposition. Reprinted in Caviness and Johnson [1998], pp. 242–268.Google Scholar
Paris, J. (1995). The Uncertain Reasoner's Companion: A Mathematical Perspective. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Schuurmans, D., & Southey, F. (2001). Local search characteristics of incomplete SAT procedures. Artificial Intelligence, 132, 121–150. Available online from: http://dx.doi.org/10.1016/S0004-3702(01)00151-5.CrossRefGoogle Scholar
Sobel, J. H. (2006). Lotteries and Miracles. Manuscript, May 2006. Available online from: http://www.scar.utoronto.ca/sobel/OnL_T/BigLotteries.wpd.pdf.Google Scholar
Strzebonski, A. (2000a). Solving algebraic inequalities with version 4. The Mathematica Journal, 7, 525–541.Google Scholar
Strzebonski, A. (2000b). Solving systems of strict polynomial inequalities. Journal of Symbolic Computation, 29, 471–480.CrossRefGoogle Scholar
Tarski, A. (1951). A Decision Method for Elementary Algebra and Geometry. Berkeley, CA: University of California Press.CrossRefGoogle Scholar
Wolfram, S. (2003). The Mathematica Book, Version 5. Cambridge: Wolfram Research.Google Scholar