Abstract
The “Most Probable World” (MPW) problem in probabilistic logic programming (PLPs) is that of finding a possible world with the highest probability. Past work has shown that this problem is computationally intractable and involves solving exponentially many linear programs, each of which is of exponential size. In this paper, we study what happens when the user focuses his interest on a set of atoms in such a PLP. We show that we can significantly reduce the number of worlds to be considered by defining a “reduced” linear program whose solution is in one-one correspondence with the exact solution to the MPW problem. However, the problem is still intractable. We develop a Monte Carlo sampling approach that enables us to build a quick approximation of the reduced linear program that allows us to estimate (inexactly) the exact solution to the MPW problem. We show experimentally that our approach works well in practice, scaling well to problems where the exact solution is intractable to compute.
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
Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilitie. Information and Computation 87(1/2), 78–128 (1990)
Hailperin, T.: Probability logic. Notre Dame J. of Formal Logic 25(3), 198–212 (1984)
Halpern, J.Y.: An analysis of first-order logics of probability. Artificial Intelligence 46(3), 311–350 (1990)
Khuller, S., Martinez, M.V., Nau, D., Simari, G., Sliva, A., Subrahmanian, V.: Computing Most Probable Worlds of Action Probabilistic Logic Programs: Scalable Estimation for 1030,000 Worlds. Annals of Mathematics and Artificial Intelligence 51(2-4), 295–331 (2007)
Khuller, S., Martinez, M.V., Nau, D., Simari, G., Sliva, A., Subrahmanian, V.: Finding most probable worlds of probabilistic logic programs. In: Prade, H., Subrahmanian, V.S. (eds.) SUM 2007. LNCS (LNAI), vol. 4772, pp. 45–59. Springer, Heidelberg (2007)
Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987)
Lukasiewicz, T.: Probabilistic logic programming. In: European Conference on Artificial Intelligence, pp. 388–392 (1998)
Mannes, A., Michael, M., Pate, A., Sliva, A., Subrahmanian, V., Wilkenfeld, J.: Stochastic opponent modelling agents: A case study with Hezbollah. In: Liu, H., Salerno, J. (eds.) Proc. 2008 First Intl. Workshop on Social Computing, Behavioral Modeling and Prediction (2008)
Mannes, A., Michel, M., Pate, A., Sliva, A., Subrahmanian, V., Wilkenfeld, J.: Stochastic opponent modeling agents: A case study with Hamas. In: Proceedings of ICCCD 2008 (2008)
Martinez, V., Simari, G., Sliva, A., Subrahmanian, V.: The soma terror organization portal (stop): Social network and analytic tools for the real-time analysis of terror groups. In: Liu, H., Salerno, J. (eds.) Proc. 2008 First Intl. Workshop on Social Computing, Behavioral Modeling and Prediction (2008)
Ng, R.T., Subrahmanian, V.S.: A semantical framework for supporting subjective and conditional probabilities in deductive databases. In: Furukawa, K. (ed.) Proceedings of the 8th International Conference on Logic Programming, pp. 565–580. The MIT Press, Cambridge (1991)
Ng, R.T., Subrahmanian, V.S.: Probabilistic logic programming. Probabilistic logic programming 102(2), 150–201 (1992)
Nilsson, N.: Probabilistic logic. Artificial Intelligence 28, 71–87 (1986)
Sliva, A., Martinez, V., Simari, G.I., Subrahmanian, V.: Soma models of the behaviors of stakeholders in the afghan drug economy: A preliminary report. In: First Int. Conference on Computational Cultural Dynamics (ICCCD 2007). ACM Press, New York (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Simari, G.I., Martinez, M.V., Sliva, A., Subrahmanian, V.S. (2008). Scaling Most Probable World Computations in Probabilistic Logic Programs. In: Greco, S., Lukasiewicz, T. (eds) Scalable Uncertainty Management. SUM 2008. Lecture Notes in Computer Science(), vol 5291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87993-0_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-87993-0_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87992-3
Online ISBN: 978-3-540-87993-0
eBook Packages: Computer ScienceComputer Science (R0)