Modelling Uncertainty in Agent Programming

  • Johan Kwisthout
  • Mehdi Dastani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3904)


Existing cognitive agent programming languages that are based on the BDI model employ logical representation and reasoning for implementing the beliefs of agents. In these programming languages, the beliefs are assumed to be certain, i.e. an implemented agent can believe a proposition or not. These programming languages fail to capture the underlying uncertainty of the agent’s beliefs which is essential for many real world agent applications. We introduce Dempster-Shafer theory as a convenient method to model uncertainty in agent’s beliefs. We show that the computational complexity of Dempster’s Rule of Combination can be controlled. In particular, the certainty value of a proposition can be deduced in linear time from the beliefs of agents, without having to calculate the combination of Dempster-Shafer mass functions.


Multiagent System Mass Function Belief Base Epistemic Logic Focal Element 
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  1. 1.
    Barnett, J.A.: Computational methods for a mathematical theory of evidence. In: Proceedings of the Seventh International Joint Conference on Artificial Intelligence, pp. 868–875 (1981)Google Scholar
  2. 2.
    Barnett, J.A.: Calculating Dempster-Shafer plausibility. IEEE transactions on pattern analysis and machine intelligence 13, 599–603 (1991)CrossRefGoogle Scholar
  3. 3.
    Braubach, L., Pokahr, A., Lamersdorf, W.: Jadex: A short overview. In: Main Conference Net.ObjectDays 2004, pp. 195–207 (September 2004)Google Scholar
  4. 4.
    Busetta, P., Ronnquist, R., Hodgson, A., Lucas, A.: Jack intelligent agents - components for intelligent agents in java. Technical report (1999)Google Scholar
  5. 5.
    Dastani, M., van Riemsdijk, B., Dignum, F., Meyer, J.-J.: A programming language for cognitive agents: Goal directed 3APL. In: Dastani, M.M., Dix, J., El Fallah-Seghrouchni, A. (eds.) PROMAS 2003. LNCS (LNAI), vol. 3067, pp. 111–130. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    de Ferreira, N.C., Fisher, M., van der Hoek, W.: A simple logic for reasoning about uncertainty. In: Proceedings of the ESSLLI 2004 Student Session, pp. 61–71 (2004)Google Scholar
  7. 7.
    Fagin, R., Halpern, J.Y.: Reasoning about knowledge and probablility. Journal of the ACM 41, 340–367 (1994)CrossRefMATHGoogle Scholar
  8. 8.
    Fattorosi-Barnaba, M., Amati, G.: Studio logica  46, 383–393 (1987)Google Scholar
  9. 9.
    Jøsang, A.: The consensus operator for combining beliefs. Artificial Intelligence Journal 142(1-2), 157–170 (2002)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Moreira, A.F., Bordini, R.H.: An operational semantics for a BDI agent-oriented programming language. In: Meyer, J.-J.C., Wooldridge, M.J. (eds.) Proceedings of the Workshop on Logics for Agent-Based Systems, pp. 45–59 (2002)Google Scholar
  11. 11.
    Orponen, P.: Dempster’s rule of combination is # P-complete. Artificial Intelligence 44, 245–253 (1990)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Rao, A.J., Georgeff, M.P.: Modelling rational agents within a BDI-architecture. In: Allen, J., Fikes, R., Sandewall, E. (eds.) Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning. Morgan Kaufmann Publishers, San Mateo (1991)Google Scholar
  13. 13.
    Sentz, K.: Combination of Evidence in Dempster-Shafer Theory. PhD thesis, Binghamton University (2002)Google Scholar
  14. 14.
    Shafer, G.: A mathematical theory of evidence. Princeton Univ. Press, Princeton (1976)MATHGoogle Scholar
  15. 15.
    Smets, P.: The combination of evidence in the transferable belief model. IEEE Pattern Analysis and Machine Intelligence 12, 447–458 (1990)CrossRefGoogle Scholar
  16. 16.
    van der Hoek, W.: Some considerations on the logic PFD. Journal of Applied Non Classical Logics 7, 287–307 (1997)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Verbeek, M.: 3APL as programming language for cognitive robotics. Master’s thesis, Utrecht University (2003)Google Scholar
  18. 18.
    Voorbraak, F.: As Far as I know - Epistemic Logic and Uncertainty. PhD thesis (1993)Google Scholar
  19. 19.
    Wilson, N.: Algorithms for dempster-shafer theory. In: Gabbay, D.M., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 5, pp. 421–475. Kluwer Academic Publishers, Algorithms (2000)CrossRefGoogle Scholar
  20. 20.
    Wooldridge, M.: Intelligent agents. In: Weiss, G. (ed.) Multiagent Systems, MIT Press, Cambridge (1999)Google Scholar
  21. 21.
    Yager, R.: On the Dempster-Shafer framework and new combination rules. Information Sciences 41, 93–137 (1987)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Johan Kwisthout
    • 1
  • Mehdi Dastani
    • 1
  1. 1.ICSUtrecht UniversityThe Netherlands

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