Skip to main content Accessibility help



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.

Corresponding author
Hide All
Basu, S., Pollack, R., & Roy, M. F. (1996). On the combinatorial and algebraic complexity of quantifier elimination. Journal of the ACM, 43, 1002–1045.
Brown, C. (2001a). Improved projection for cylindrical algebraic decomposition. Journal of Symbolic Computation, 32, 447–465.
Brown, C. (2001b). Simple CAD construction and its applications. Journal of Symbolic Computation, 31, 521–547.
Caviness, B., & Johnson, J., editors. (1998). Quantifier Elimination and Cylindrical Algebraic Decomposition. Vienna: Springer-Verlag.
Collins, G. (1975). Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Reprinted in Caviness and Johnson [1998], pp. 85–121.
Davenport, J. H., & Heintz, J. (1988). Real quantifier elimination is doubly exponential. Journal of Symbolic Computation, 5, 29–35.
Feferman, A. B., & Feferman, S. (2004). Alfred Tarski: Life and Logic. Cambridge: Cambridge University Press.
Feller, W. (1968). An Introduction to Probability Theory and Its Applications (third edition), vol. 1. New York: John Wiley & Sons Inc.
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:
Fitelson, B. (2001a). A Bayesian account of independent evidence with applications. Philosophy of Science, 68, S123–S140. Available online from:
Fitelson, B. (2001b). Studies in Bayesian confirmation theory. PhD Thesis, University of Wisconsin – Madison (Philosophy). Available online from:
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:
Hong, H. (1990). An improvement of the projection operator in cylindrical algebraic decomposition. Reprinted in Caviness and Johnson [1998], pp. 166–173.
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:
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.
Hong, H. (2006). QEPCAD – Quantifier elimination by partial cylindrical algebraic decomposition. Computer Program Web site. Available online from:
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.
Joyce, J. (2003). Bayes's Theorem. The Stanford Encyclopedia of Philosophy. Available online from:
Kolmogorov, A. (1956). Foundations of Probability (second edition). New York: AMS Chelsea.
McCallum, S. (1998). An improved projection operator for cylindrical algebraic decomposition. Reprinted in Caviness and Johnson [1998], pp. 242–268.
Paris, J. (1995). The Uncertain Reasoner's Companion: A Mathematical Perspective. Cambridge: Cambridge University Press.
Schuurmans, D., & Southey, F. (2001). Local search characteristics of incomplete SAT procedures. Artificial Intelligence, 132, 121–150. Available online from:
Sobel, J. H. (2006). Lotteries and Miracles. Manuscript, May 2006. Available online from:
Strzebonski, A. (2000a). Solving algebraic inequalities with version 4. The Mathematica Journal, 7, 525–541.
Strzebonski, A. (2000b). Solving systems of strict polynomial inequalities. Journal of Symbolic Computation, 29, 471–480.
Tarski, A. (1951). A Decision Method for Elementary Algebra and Geometry. Berkeley, CA: University of California Press.
Wolfram, S. (2003). The Mathematica Book, Version 5. Cambridge: Wolfram Research.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed