A Probabilistic Semantics for Cognitive Maps

  • Aymeric Le DorzeEmail author
  • Béatrice Duval
  • Laurent Garcia
  • David Genest
  • Philippe Leray
  • Stéphane Loiseau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8946)


Cognitive maps are a graphical knowledge representation model that describes influences between concepts, each influence being quantified by a value. Most cognitive map models use values the semantics of which is not formally defined. This paper introduces the probabilistic cognitive maps, a new cognitive map model where the influence values are assumed to be probabilities. We formally define this model and redefine the propagated influence, an operation that computes the global influence between two concepts in the map, to be in accordance with this semantics. To prove the soundness of our model, we propose a method to represent any probabilistic cognitive map as a Bayesian network.


Cognitive map Probabilities Causality Bayesian network 


  1. 1.
    Axelrod, R.M.: Structure of Decision: The Cognitive Maps of Political Elites. Princeton University Press, Princeton (1976)Google Scholar
  2. 2.
    Tolman, E.C.: Cognitive maps in rats and men. Psychol. Rev. 55(4), 189–208 (1948)CrossRefGoogle Scholar
  3. 3.
    Celik, F.D., Ozesmi, U., Akdogan, A.: Participatory ecosystem management planning at Tuzla Lake (Turkey) using Fuzzy cognitive mapping (2005). eprint arXiv:q-bio/0510015
  4. 4.
    Levi, A., Tetlock, P.E.: A cognitive analysis of Japan’s 1941 decision for war. J. Confl. Resolut. 24, 195–211 (1980)CrossRefGoogle Scholar
  5. 5.
    Zhou, S., Zhang, J.Y., Liu, Z.Q.: Quotient FCMs - a decomposition theory for Fuzzy cognitive maps. IEEE Trans. Fuzzy Syst. 11, 593–604 (2003)CrossRefGoogle Scholar
  6. 6.
    Kosko, B.: Fuzzy cognitive maps. Int. J. Man-Mach. Stud. 24, 65–75 (1986)CrossRefzbMATHGoogle Scholar
  7. 7.
    Satur, R., Liu, Z.Q.: A contextual Fuzzy cognitive map framework for geographic information systems. IEEE Trans. Fuzzy Syst. 7, 481–494 (1999)CrossRefGoogle Scholar
  8. 8.
    Aguilar, J.: A survey about Fuzzy cognitive maps papers. Int. J. Comput. Cogn. 3, 27–33 (2005)Google Scholar
  9. 9.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)zbMATHGoogle Scholar
  10. 10.
    Pearl, J.: Causality: Models, Reasoning and Inference, 2nd edn. Cambridge University Press, New York (2009)CrossRefzbMATHGoogle Scholar
  11. 11.
    Song, H.J., Shen, Z.Q., Miao, C.Y., Liu, Z.Q., Miao, Y.: Probabilistic Fuzzy cognitive map. In: FUZZ-IEEE 2006, pp. 1221–1228. IEEE (2006)Google Scholar
  12. 12.
    Krichéne, J., Boudriga, N.: Incident response probabilistic cognitive maps. In: Proceedings of the IEEE International Symposium on Parallel and Distributed Processing with Applications (ISPA 2008), pp. 689–694. IEEE, Los Alamitos (2008)Google Scholar
  13. 13.
    Wellman, M.P.: Fundamental concepts of qualitative probabilistic networks. Artif. Intell. 44, 257–303 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lionel, C., David, G., Aymeric, L.D., Stéphane, L.: User centered cognitive maps. In: Guillet, F., Pinaud, B., Venturini, G., Zighed, D.A. (eds.) Advances in Knowledge Discovery and Management. SCI, vol. 471, pp. 203–220. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  15. 15.
    Genest, D., Loiseau, S.: Modélisation, classification et propagation dans des réseaux d’influence. Technique et Science Informatiques 26, 471–496 (2007)CrossRefGoogle Scholar
  16. 16.
    Cooper, G.F.: The computational complexity of probabilistic inference using Bayesian belief networks. Artif. Intell. 42, 393–405 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Charniak, E., McDermott, D.: Introduction to Artificial Intelligence. Addison-Wesley, Reading (1985) zbMATHGoogle Scholar
  18. 18.
    Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, vol. 1. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  19. 19.
    Cheah, W.P., Kim, K.-Y., Yang, H.-J., Choi, S.-Y., Lee, H.-J.: A manufacturing-environmental model using Bayesian belief networks for assembly design decision support. In: Okuno, H.G., Ali, M. (eds.) IEA/AIE 2007. LNCS (LNAI), vol. 4570, pp. 374–383. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  20. 20.
    Sedki, K., Bonneau de Beaufort, L.: Cognitive maps and Bayesian networks for knowledge representation and reasoning. In: ICTAI 2012, pp. 1035–1040. IEEE (2012)Google Scholar
  21. 21.
    Nadkarni, S., Shenoy, P.P.: A Bayesian network approach to making inferences in causal maps. Eur. J. Oper. Res. 128, 479–498 (2001)CrossRefzbMATHGoogle Scholar
  22. 22.
    Nadkarni, S., Shenoy, P.P.: A causal mapping approach to constructing Bayesian networks. Decis. Support Syst. 38, 259–281 (2004)CrossRefGoogle Scholar
  23. 23.
    Lemmer, J.F., Gossink, D.E.: Recursive noisy or - a rule for estimating complex probabilistic interactions. Trans. Syst. Man Cybern. Part B 34, 2252–2261 (2004)CrossRefGoogle Scholar
  24. 24.
    Das, B.: Generating conditional probabilities for Bayesian networks: easing the knowledge acquisition problem. CoRR cs.AI/0411034 (2004)Google Scholar
  25. 25.
    Le Dorze, A., Duval, B., Garcia, L., Genest, D., Leray, P., Loiseau, S.: Probabilistic cognitive maps. Technical report, LERIA, Université d’Angers (2013)Google Scholar
  26. 26.
    Le Dorze, A., Garcia, L., Genest, D., Loiseau, S.: Validation of a cognitive map. In: Duval, B., van den Herik, J., Loiseau, S., Filipe, J. (eds.) ICAART 2014, vol. 1 of Science and Technology Publications, pp. 320–327. SCITEPRESS (2014)Google Scholar
  27. 27.
    Renooij, S., van der Gaag, L. C.: From qualitative to quantitative probabilistic networks. In: Darwiche, A., Friedman, N. (eds.) UAI 2002, pp. 422–429. Morgan Kaufmann (2002)Google Scholar
  28. 28.
    Renooij, S., Parsons, S., Pardieck, P.: Using kappas as indicators of strength in qualitative probabilistic networks. In: Nielsen, T.D., Zhang, N.L. (eds.) ECSQARU 2003. LNCS (LNAI), vol. 2711, pp. 87–99. Springer, Heidelberg (2003) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Aymeric Le Dorze
    • 1
    Email author
  • Béatrice Duval
    • 1
  • Laurent Garcia
    • 1
  • David Genest
    • 1
  • Philippe Leray
    • 2
  • Stéphane Loiseau
    • 1
  1. 1.Laboratoire d’Étude et de Recherche en Informatique d’AngersUniversité d’AngersAngers Cedex 01France
  2. 2.Laboratoire d’Informatique de Nantes Atlantique, École PolytechniqueUniversité de NantesNantes Cedex 3France

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