Abstract
We present a language for integrating probabilistic reasoning and logic programming. The key idea is to use constraints based techniques such as the constraints store and finite domain variables. First we show how these techniques can be used to integrate a number of probabilistic inference algorithms with logic programming. We then proceed to detail a language which effects conditioning by probabilistically partitioning the constraint store. We elucidate the kinds of reasoning effected by the introduced language by means of two well known probabilistic problems: the three prisoners and Monty Hall. In particular we show how the syntax of the language can be used to avoid the pitfalls normally associated with the two problems. An elimination algorithm for computing the probability of a query in a given store is presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Angelopoulos, N.: Probabilistic Finite Domains. Ph.D. thesis, Department of Computing, City University, London, UK (2001)
Angelopoulos, N.: clp(pfd(Y)): Constraints for probabilistic reasoning in logic programming. In: Ninth International Conference on Principles and Practice of Constraint Programming Kinsale, Ireland (2003)
Baldwin, J.F.: Evidential support logic programming. Journal of Fuzzy Sets and Systems 24, 1–26 (1987)
Costa, V., Page, D., Qazi, M., Cussens, J.: CLP(\(\mathcal{BN}\)) constraint logic programming for probabilistic knowledge. In: 19th Annual Conference on Uncertainty in AI, Acapulco, Mexico, pp. 517–524 (2002)
Cussens, J.: Stochastic logic programs: Sampling, inference and applications. In: 16th Annual Conference on Uncertainty in AI, San Francisco, USA, pp. 115–122 (2000)
Dechter, R.: Bucket elimination: A unifying framework for probabilistic inference. In: Proceedings of Uncertainty in AI (UAI 1996), Portland, USA (1996); Extended version in Dechter99
Dechter, R. Larkin, D. Hybrid processing of beliefs and constraints. In: Proceedings of Uncertainty in AI (UAI 2001). Extended version in Dechter2001a
Grinstead, C.M., Snell, J.L.: Introduction to Probability (Second Revised Edition) American Mathematical Society
Grünwald, P., Halpern, J.: Updating probabilities. Journal of AI Research 19, 243–278 (2003)
Kyburg, H.E.: The reference class. Philosophy of Science 50, 374–397 (1983)
Kyburg, H.E.: Uncertain inferences and uncertain conclusions. In: 12th Annual Conference on Uncertainty in AI, pp. 365–372 (1996)
Hogger, C.J.: Essentials of Logic Programming. Oxford University Press, Oxford (1990)
Jaffar, J., Lassez, J.-L.: Constraint logic programming. In: POPL 1987: Proceedings 14th ACM Symposium on Principles of Programming Languages, Munich, pp. 111–119. ACM, New York (1987)
Kameya, Y., Sato, T.: Efficient learning with tabulation for parameterized logic programs. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 269–294. Springer, Heidelberg (2000)
Lukasiewicz, T.: Probabilistic logic programming. In: 13th Biennial European Conference on Artificial Intelligence, Brighton, UK, pp. 388–392 (1999)
Lukasiewicz, T.: Probabilistic logic programming under inheritance with overriding. In: 17th Conference on Uncertainty in Artificial Intelligence (UAI-2001), Seattle, Washington, USA, pp. 329–336 (2001)
Montanari, U.: Networks of constraints: Fundamental properties and applications to picture processing. Information Sciences 7, 95–132 (1974)
Mosteller, F.: Fifty challenging problems in probability, with solutions. Addison-Wesley, Reading (1965)
Ng, R., Subrahmanian, V.: Probabilistic logic programming. Information and Computation 101, 150–201 (1992)
Pollock, J.L.: The theory of nomic probability. Synthese 90, 263–300 (1992)
Poole, D.: Probabilistic horn abduction and bayesian networks. Artificial Intelligence 64, 81–129 (1993)
Riezler, S.: Probabilistic Constraint Logic Programming. Ph.D. thesis, Neuphilologische Fakultät, Universität Tübingen, Tubingen, Germany (1998)
Saraswat, V.: The category of constraint systems is Cartesian-closed. In: Proceedings, Seventh Annual IEEE Symposium on Logic in Computer Science, Santa Cruz, California, IEEE Computer Society Press, Los Alamitos (1992)
vos Savant, M.: Ask Marilyn. St. Martins, New York (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Angelopoulos, N. (2004). Probabilistic Space Partitioning in Constraint Logic Programming. In: Maher, M.J. (eds) Advances in Computer Science - ASIAN 2004. Higher-Level Decision Making. ASIAN 2004. Lecture Notes in Computer Science, vol 3321. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30502-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-30502-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24087-7
Online ISBN: 978-3-540-30502-6
eBook Packages: Computer ScienceComputer Science (R0)