Advertisement

Abstract

Logic and probability theory are two of the most important branches of mathematics and each has played a significant role in artificial intelligence (AI) research. Beginning with Leibniz, scholars have attempted to unify logic and probability. For “classical” AI, based largely on first-order logic, the purpose of such a unification is to handle uncertainty and facilitate learning from real data; for “modern” AI, based largely on probability theory, the purpose is to acquire formal languages with sufficient expressive power to handle complex domains and incorporate prior knowledge. This paper provides a brief summary of an invited talk describing efforts in these directions, focusing in particular on open-universe probability models that allow for uncertainty about the existence and identity of objects.

Keywords

first-order logic probability probabilistic programming Bayesian logic machine learning 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arora, N., Russell, S., de Salvo Braz, R., Sudderth, E.: Gibbs sampling in open-universe stochastic languages. In: UAI 2010 (2010)Google Scholar
  2. 2.
    Arora, N.S., Russell, S., Sudderth, E.: NET-VISA: Network processing vertically integrated seismic analysis. Bull. Seism.  Soc. Amer. 103 (2013)Google Scholar
  3. 3.
    Bacchus, F.: Representing and Reasoning with Probabilistic Knowledge. MIT Press (1990)Google Scholar
  4. 4.
    Bessière, P., Mazer, E., Ahuactzin, J.M., Mekhnacha, K.: Bayesian programming. CRC (2013)Google Scholar
  5. 5.
    Breese, J.S.: Construction of belief and decision networks. Computational Intelligence 8, 624–647 (1992)CrossRefGoogle Scholar
  6. 6.
    Darroch, J.N., Lauritzen, S.L., Speed, T.P.: Markov fields and log-linear interaction models for contingency tables. The Annals of Statistics 8(3), 522–539 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Gilks, W.R., Thomas, A., Spiegelhalter, D.J.: A language and program for complex Bayesian modelling. The Statistician 43, 169–178 (1994)CrossRefGoogle Scholar
  8. 8.
    Hailperin, T.: Probability logic. Notre Dame J. Formal Logic 25(3), 198–212 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Halpern, J.Y.: An analysis of first-order logics of probability. AIJ 46(3), 311–350 (1990)zbMATHGoogle Scholar
  10. 10.
    Howson, C.: Probability and logic. J. Applied Logic 1(3-4), 151–165 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Kersting, K., De Raedt, L.: Bayesian logic programs. In: ILP 2000 (2000)Google Scholar
  12. 12.
    Koller, D., Pfeffer, A.: Probabilistic frame-based systems. In: AAAI 1998 (1998)Google Scholar
  13. 13.
    Li, L., Ramsundar, B., Russell, S.: Dynamic scaled sampling for deterministic constraints. In: AI/Stats 2013 (2013)Google Scholar
  14. 14.
    Lukasiewicz, T.: Probabilistic logic programming. In: ECAI (1998)Google Scholar
  15. 15.
    McCallum, A., Schultz, K., Singh, S.: FACTORIE: Probabilistic programming via imperatively defined factor graphs. NIPS 22 (2010)Google Scholar
  16. 16.
    McCarthy, J.: Programs with common sense. In: Proc. Symposium on Mechanisation of Thought Processes. Her Majesty’s Stationery Office (1958)Google Scholar
  17. 17.
    Milch, B.: Probabilistic Models with Unknown Objects. Ph.D. thesis, UC Berkeley (2006)Google Scholar
  18. 18.
    Milch, B., Marthi, B., Sontag, D., Russell, S.J., Ong, D., Kolobov, A.: BLOG: Probabilistic models with unknown objects. In: IJCAI 2005 (2005)Google Scholar
  19. 19.
    Milch, B., Russell, S.: Extending Bayesian networks to the open-universe case. In: Dechter, R., Geffner, H., Halpern, J. (eds.) Heuristics, Probability and Causality: A Tribute to Judea Pearl. College Publications (2010)Google Scholar
  20. 20.
    Milch, B., Russell, S.J.: General-purpose MCMC inference over relational structures. In: UAI 2006 (2006)Google Scholar
  21. 21.
    Pasula, H., Marthi, B., Milch, B., Russell, S.J., Shpitser, I.: Identity uncertainty and citation matching. NIPS 15 (2003)Google Scholar
  22. 22.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann (1988)Google Scholar
  23. 23.
    Poole, D.: Probabilistic Horn abduction and Bayesian networks. AIJ 64, 81–129 (1993)zbMATHGoogle Scholar
  24. 24.
    Poole, D.: First-order probabilistic inference. In: IJCAI 2003 (2003)Google Scholar
  25. 25.
    Sato, T., Kameya, Y.: PRISM: A symbolic statistical modeling language. In: IJCAI 1997 (1997)Google Scholar
  26. 26.
    Van den Broeck, G.: Lifted Inference and Learning in Statistical Relational Models. Ph.D. thesis, Katholieke Universiteit Leuven (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Stuart Russell
    • 1
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.Laboratoire d’informatique de Paris 6Université Pierre et Marie CurieParis Cedex 05France

Personalised recommendations