Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Probabilistic Logic and Relational Models

  • Manfred Jaeger
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_157

Synonyms

Glossary

First-Order Predicate Logic

Formal system of mathematical logic that supports reasoning about structures consisting of a domain on which certain relations and functions are defined

Bayesian Network

A graphical representation for the joint probability distribution of a set of random variables. A Bayesian network is specified by a directed acyclic graph whose nodes are the random variables and the conditional probability distributions of the random variables given their parents in the graph

Markov Network

A graphical representation for the joint probability distribution of a set of random variables. A Markov network is specified by an undirected graph whose nodes are the random variables and potential functions defined on the cliques of the graph

Horn Clause

A special class of “ifthen” expressions in first-order predicate logic, where the ifcondition is a conjunction...

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References

  1. Blockeel H, De Raedt L (1998) Top-down induction of first-order logical decision trees. Artif Intell 101(1–2):285–297MathSciNetzbMATHCrossRefGoogle Scholar
  2. Breese JS (1992) Construction of belief and decision networks. Comput Intell 8(4):624–647CrossRefGoogle Scholar
  3. Breese JS, Goldman RP, Wellman MP (1994) Introduction to the special section on knowledge-based construction of probabilistic decision models. IEEE Trans Syst Man Cybern 24(11):1577–1579Google Scholar
  4. Chavira M, Darwiche A (2008) On probabilistic inference by weighted model counting. Artif Intell 172:772–799MathSciNetzbMATHCrossRefGoogle Scholar
  5. de Salvo Braz R, Amir E, Roth D (2005) Lifted first-order probabilistic inference. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI-05), pp 1319–1325Google Scholar
  6. Fierens D, den Broeck GV, Thon I, Gutmann B, De Raedt L (2011) Inference in probabilistic logic programs using weighted CNF’s. In: Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence (UAI 2011). AUAI Press, CorvallisGoogle Scholar
  7. Friedman N, Getoor L, Koller D, Pfeffer A (1999) Learning probabilistic relational models. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI-99)Google Scholar
  8. Gilks WR, Thomas A, Spiegelhalter DJ (1994) A language and program for complex bayesian modelling. Statistician 43(1):169–177CrossRefGoogle Scholar
  9. Gogate V, Domingos P (2011) Probabilistic theorem proving. In: Proceedings of the 27th Conference of Uncertainty in Artificial Intelligence (UAI-11). AUAI Press, CorvallisGoogle Scholar
  10. Goodman ND, Mansinghka VK, Roy D, Bonawitz K, Tenenbaum JB (2008) Church: a language for generative models. In: Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence (UAI-08). AUAI Press, CorvallisGoogle Scholar
  11. Haddawy P (1994) Generating Bayesian networks from probability logic knowledge bases. In: Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence (UAI-94). Morgan Kaufmann, San Francisco, pp 262–269Google Scholar
  12. Halpern J (1990) An analysis of first-order logics of probability. Artif Intell 46:311–350MathSciNetzbMATHCrossRefGoogle Scholar
  13. Heckerman D, Meek C, Koller D (2007) Probabilistic entity-relationship models, PRMs, and plate models. In: Getoor L, Taskar B (eds) Introduction to statistical relational learning. MIT Press, Cambridge, MAGoogle Scholar
  14. Jaeger M (1997) Relational bayesian networks. In: Geiger D, Shenoy PP (eds) Proceedings of the 13th Conference of Uncertainty in Artificial Intelligence (UAI-97). Morgan Kaufmann, San Francisco, pp 266–273Google Scholar
  15. Jaeger M (2000) On the complexity of inference about probabilistic relational models. Artif Intell 117:297–308MathSciNetzbMATHCrossRefGoogle Scholar
  16. Kersting K, De Raedt L (2001) Towards combining inductive logic programming and bayesian networks. In: Proceedings of the Eleventh International Conference on Inductive Logic Programming (ILP-2001). Springer, Berlin, Heidelberg, pp 118–131zbMATHCrossRefGoogle Scholar
  17. Kimmig A, Demoen B, De Raedt L, Santos Costa V, Rocha R (2011) On the implementation of the probabilistic logic programming language problog. Theory Pract Logic Program 11(2–3):235–262MathSciNetzbMATHCrossRefGoogle Scholar
  18. Laskey KB (2008) Mebn: a language for first-order bayesian knowledge bases. Artif Intell 172(2–3):140–178.  https://doi.org/10.1016/j.artint.2007.09.006MathSciNetCrossRefzbMATHGoogle Scholar
  19. Laskey KB, Mahoney SM (1997) Network fragments: representing knowledge for constructing probabilistic models. In: Proceedings of the 13th Annual Conference on Uncertainty in Artificial Intelligence (UAI–97). Morgan Kaufmann Publishers, San Francisco, pp 334–341Google Scholar
  20. Milch B, Marthi B, Russell S, Sontag D, Ong D, Kolobov A (2005) Blog: probabilistic logic with unknown objects. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI-05), pp 1352–1359Google Scholar
  21. Milch B, Zettlemoyer LS, Kersting K, Haimes M, Kaelbling LP (2008) Lifted probabilistic inference with counting formulas. In: Proceedings of the 23rd AAAI Conference on Artificial Intelligence (AAAI-08). AAAI Press, Menlo ParkGoogle Scholar
  22. Muggleton S (1996) Stochastic logic programs. In: De Raedt L (ed) Advances in Inductive Logic Programming. IOS Press, Washington, DC, pp 254–264Google Scholar
  23. Neville J, Jensen D, Friedland L, Hay M (2003) Learning relational probability trees. In: Proceedings of The 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-03). ACM, New YorkGoogle Scholar
  24. Ng KS, Lloyd JW, Uther WTB (2008) Probabilistic modelling, inference and learning using logical theories. Ann Math Artif Intell 54(1–3):159–205MathSciNetzbMATHCrossRefGoogle Scholar
  25. Ngo L, Haddawy P (1997) Answering queries from context-sensitive probabilistic knowledge bases. Theor Comput Sci 171:147–177MathSciNetzbMATHCrossRefGoogle Scholar
  26. Nilsson N (1986) Probabilistic logic. Artif Intell 28:71–88MathSciNetzbMATHCrossRefGoogle Scholar
  27. Pfeffer A (2001) IBAL: a probabilistic rational programming language. In: Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI-01)Google Scholar
  28. Poole D (1993) Probabilistic horn abduction and Bayesian networks. Artif Intell 64:81–129zbMATHCrossRefGoogle Scholar
  29. Poole D (2003) First-order probabilistic inference. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI-03)Google Scholar
  30. Poole D (2008) The independent choice logic and beyond. In: De Raedt L, Frasconi P, Kersting K, Muggleton S (eds) Probabilistic inductive logic programming, lecture notes in artificial intelligence, vol 4911. Springer, Berlin, pp 222–243CrossRefGoogle Scholar
  31. Richardson M, Domingos P (2006) Markov logic networks. Mach Learn 62(1–2):107–136CrossRefGoogle Scholar
  32. Robins G, Pattison P, Kalish Y, Lusher D (2007) An introduction to exponential random graph (p*) models for social networks. Soc Networks 29(2):173–191CrossRefGoogle Scholar
  33. Sato T (1995) A statistical learning method for logic programs with distribution semantics. In: Proceedings of the 12th International Conference on Logic Programming (ICLP’95). MIT Press, Cambridge, pp 715–729Google Scholar
  34. Van den Broeck G, Taghipour N, Meert W, Davis J, De Raedt L (2011) Lifted probabilistic inference by first-order knowledge compilation. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI-11)Google Scholar

Recommended Reading

  1. De Raedt L (2008) Logical and relational learning. Springer, BerlinzbMATHCrossRefGoogle Scholar
  2. De Raedt L, Frasconi P, Kersting K, Muggleton S (eds) (2008) Probabilistic inductive logic programming, lecture notes in artificial intelligence, vol 4911. Springer, BerlinGoogle Scholar
  3. Getoor L, Taskar B (eds) (2007) Introduction to statistical relational learning. MIT Press, Cambridge, MAzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceAalborg UniversityAalborgDenmark

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates