Advertisement

The Independent Choice Logic and Beyond

  • David Poole
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4911)

Abstract

The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a logic program that gives the consequences of the choices. There is a measure over possible worlds that is defined by the probabilities of the independent choices, and what is true in each possible world is given by choices made in that world and the logic program. ICL is interesting because it is a simple, natural and expressive representation of rich probabilistic models. This paper gives an overview of the work done over the last decade and half, and points towards the considerable work ahead, particularly in the areas of lifted inference and the problems of existence and identity.

Keywords

Bayesian Network Logic Program Logic Programming Predicate Symbol Inductive Logic Programming 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allen, D., Darwiche, A.: New advances in inference by recursive conditioning. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI 2003), pp. 2–10. Morgan Kaufmann, San Francisco (2003)Google Scholar
  2. Andre, D., Russell, S.: State abstraction for programmable reinforcement learning agents. In: Proc. AAAI 2002 (2002)Google Scholar
  3. Apt, K.R., Bezem, M.: Acyclic programs. New Generation Computing 9(3-4), 335–363 (1991)Google Scholar
  4. Baral, C., Gelfond, M., Rushton, N.: Probabilistic reasoning with answer sets. In: Proceedings of LPNMR7, pp. 21–33 (2004)Google Scholar
  5. Boutilier, C., Friedman, N., Goldszmidt, M., Koller, D.: Context-specific independence in Bayesian networks. In: Horvitz, E., Jensen, F. (eds.) UAI 1996, Portland, OR, pp. 115–123 (1996)Google Scholar
  6. Brown, J.S., Burton, R.R.: Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science 2, 155–191 (1978)CrossRefGoogle Scholar
  7. Buntine, W.L.: Operations for learning with graphical models. Journal of Artificial Intelligence Research 2, 159–225 (1994)Google Scholar
  8. Chang, C.L., Lee, R.C.T.: Symbolic Logical and Mechanical Theorem Proving. Academic Press, New York (1973)Google Scholar
  9. Chavira, M., Darwiche, A., Jaeger, M.: Compiling relational bayesian networks for exact inference. International Journal of Approximate Reasoning (IJAR) 42, 4–20 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  10. Chickering, D.M., Heckerman, D., Meek, C.: A Bayesian approach to learning Bayesian networks with local structure. In: UAI 1997, pp. 80–89 (1997)Google Scholar
  11. Clark, K.L.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Databases, pp. 293–322. Plenum Press, New York (1978)Google Scholar
  12. Cobba, B.R., Shenoy, P.P.: Inference in hybrid bayesian networks with mixtures of truncated exponentials. International Journal of Approximate Reasoning 41(3), 257–286 (2006)CrossRefMathSciNetGoogle Scholar
  13. Cozman, F., Krotkov, E.: Truncated gaussians as tolerance sets. Technical Report CMU-RI-TR-94-35, Robotics Institute, Carnegie Mellon University, Pittsburgh, PA (September 1994)Google Scholar
  14. Darwiche, A.: Recursive conditioning. Artificial Intelligence 126(1-2), 5–41 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  15. de Salvo Braz, R., Amir, E., Roth, D.: Lifted first-order probabilistic inference. In: IJCAI 2005, Edinburgh (2005), http://www.cs.uiuc.edu/~eyal/papers/fopl-res-ijcai05.pdf
  16. Díez, F.J., Galán, S.F.: Efficient computation for the noisy max. International Journal of Intelligent Systems (to appear, 2002)Google Scholar
  17. Friedman, N., Goldszmidt, M.: Learning Bayesian networks with local structure. In: UAI 1996, pp. 252–262 (1996), http://www2.sis.pitt.edu/~dsl/UAI/UAI96/Friedman1.UAI96.html
  18. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Proceedings of the Fifth Logic Programming Symposium, Cambridge, MA, pp. 1070–1080 (1988)Google Scholar
  19. Getoor, L., Friedman, N., Koller, D., Pfeffer, A.: Learning probabilistic relational models. In: Dzeroski, S., Lavrac, N. (eds.) Relational Data Mining, pp. 307–337. Springer, Heidelberg (2001)Google Scholar
  20. Heckerman, D.: A tutorial on learning with Bayesian networks. Technical Report MSR-TR-95-06, Microsoft Research, March 1995. URL Revised (November 1996), http://www.research.microsoft.com/research/dtg/heckerma/heckerma.html
  21. Heckerman, D., Meek, C., Koller, D.: Probabilistic models for relational data. Technical Report MSR-TR-2004-30, Microsoft Research (March 2004)Google Scholar
  22. Horsch, M., Poole, D.: A dynamic approach to probabilistic inference using Bayesian networks. In: Proc. Sixth Conference on Uncertainty in AI, Boston, July 1990, pp. 155–161 (1990)Google Scholar
  23. Kersting, K., De Raedt, L.: Bayesian logic programming: Theory and tool. In: Getoor, L., Taskar, B. (eds.) An Introduction to Statistical Relational Learning, MIT Press, Cambridge (2007)Google Scholar
  24. Laskey, K.B., da Costa, P.G.C.: Of klingons and starships: Bayesian logic for the 23rd century. In: Uncertainty in Artificial Intelligence: Proceedings of the Twenty-First Conference (2005)Google Scholar
  25. Lifschitz, V.: Answer set programming and plan generation. Artificial Intelligence 138(1–2), 39–54 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  26. Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Symbolic Computation Series. Springer, Berlin (1987)zbMATHGoogle Scholar
  27. Milch, B., Marthi, B., Russell, S., Sontag, D., Ong, D.L., Kolobov, A.: BLOG: Probabilistic models with unknown objects. In: IJCAI 2005, Edinburgh (2005)Google Scholar
  28. Muggleton, S.: Stochastic logic programs. In: De Raedt, L. (ed.) Advances in Inductive Logic Programming, pp. 254–264. IOS Press, Amsterdam (1996)Google Scholar
  29. Muggleton, S.: Inverse entailment and Progol. New Generation Computing 13(3-4), 245–286 (1995)Google Scholar
  30. Muggleton, S., De Raedt, L.: Inductive logic programming: Theory and methods. Journal of Logic Programming 19(20), 629–679 (1994)CrossRefMathSciNetGoogle Scholar
  31. Neumann, J.V., Morgenstern, O.: Theory of Games and Economic Behavior, 3rd edn. Princeton University Press, Princeton (1953)zbMATHGoogle Scholar
  32. Nilsson, N.J.: Logic and artificial intelligence. Artificial Intelligence 47, 31–56 (1991)CrossRefMathSciNetGoogle Scholar
  33. Pasula, H., Marthi, B., Milch, B., Russell, S., Shpitser, I.: Identity uncertainty and citation matching. In: NIPS, vol. 15 (2003)Google Scholar
  34. Pearl, J.: Causality: Models, Reasoning and Inference. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  35. Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)Google Scholar
  36. Pfeffer, A.: IBAL: A probabilistic rational programming language. In: IJCAI 2001 (2001), http://www.eecs.harvard.edu/~avi/Papers/ibal.ijcai01.ps
  37. Poole, D.: Logical generative models for probabilistic reasoning about existence, roles and identity. In: 22nd AAAI Conference on AI (AAAI 2007) (2007)Google Scholar
  38. Poole, D.: Learning, Bayesian probability, graphical models, and abduction. In: Flach, P., Kakas, A. (eds.) Abduction and Induction: Essays on their relation and integration, Kluwer, Dordrecht (2000a)Google Scholar
  39. Poole, D.: First-order probabilistic inference. In: Proc. Eighteenth International Joint Conference on Artificial Intelligence (IJCAI 2003), Acapulco, Mexico, pp. 985–991 (2003)Google Scholar
  40. Poole, D.: Explanation and prediction: An architecture for default and abductive reasoning. Computational Intelligence 5(2), 97–110 (1989)CrossRefMathSciNetGoogle Scholar
  41. Poole, D.: A methodology for using a default and abductive reasoning system. International Journal of Intelligent Systems 5(5), 521–548 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  42. Poole, D.: Representing diagnostic knowledge for probabilistic Horn abduction. In: IJCAI 1991, Sydney, pp. 1129–1135 (August 1991a)Google Scholar
  43. Poole, D.: Representing Bayesian networks within probabilistic Horn abduction. In: UAI 1991, Los Angeles, July 1991, pp. 271–278 (1991b)Google Scholar
  44. Poole, D.: Logic programming, abduction and probability: A top-down anytime algorithm for computing prior and posterior probabilities. New Generation Computing 11(3–4), 377–400 (1993a)zbMATHGoogle Scholar
  45. Poole, D.: Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence 64(1), 81–129 (1993b)zbMATHCrossRefGoogle Scholar
  46. Poole, D.: Probabilistic conflicts in a search algorithm for estimating posterior probabilities in Bayesian networks. Artificial Intelligence 88, 69–100 (1996)zbMATHCrossRefGoogle Scholar
  47. Poole, D.: Probabilistic partial evaluation: Exploiting rule structure in probabilistic inference. In: IJCAI 1997, Nagoya, Japan, pp. 1284–1291 (1997a), http://www.cs.ubc.ca/spider/poole/abstracts/pro-pa.html
  48. Poole, D.: The independent choice logic for modelling multiple agents under uncertainty. Artificial Intelligence 94, 7–56 (special issue on economic principles of multi-agent systems) (1997b), http://www.cs.ubc.ca/spider/poole/abstracts/icl.html
  49. Poole, D.: Abducing through negation as failure: stable models in the Independent Choice Logic. Journal of Logic Programming 44(1–3), 5–35 (2000), http://www.cs.ubc.ca/spider/poole/abstracts/abnaf.html zbMATHCrossRefMathSciNetGoogle Scholar
  50. Poole, D., Zhang, N.L.: Exploiting contextual independence in probabilistic inference. Journal of Artificial Intelligence Research 18, 263–313 (2003)zbMATHMathSciNetGoogle Scholar
  51. Poole, D., Mackworth, A., Goebel, R.: Computational Intelligence: A Logical Approach. Oxford University Press, New York (1998)zbMATHGoogle Scholar
  52. Quinlan, J.R., Cameron-Jones, R.M.: Induction of logic programs: FOIL and related systems. New Generation Computing 13(3-4), 287–312 (1995)CrossRefGoogle Scholar
  53. Richardson, M., Domingos, P.: Markov logic networks. Machine Learning 62, 107–136 (2006)CrossRefGoogle Scholar
  54. Sato, T., Kameya, Y.: Parameter learning of logic programs for symbolic-statistical modeling. Journal of Artificial Intelligence Research (JAIR) 15, 391–454 (2001)zbMATHMathSciNetGoogle Scholar
  55. Savage, L.J.: The Foundation of Statistics, 2nd edn. Dover, New York (1972)Google Scholar
  56. Shanahan, M.: Prediction is deduction, but explanation is abduction. In: IJCAI-1989, Detroit, MI, pp. 1055–1060 (August 1989)Google Scholar
  57. Thrun, S.: Towards programming tools for robots that integrate probabilistic computation and learning. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, IEEE, Los Alamitos (2000)Google Scholar
  58. Zhang, N.L., Poole, D.: Exploiting causal independence in Bayesian network inference. Journal of Artificial Intelligence Research 5, 301–328 (1996)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • David Poole
    • 1
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

Personalised recommendations