Minds and Machines

, Volume 18, Issue 2, pp 273–288 | Cite as

The Metaphysical Character of the Criticisms Raised Against the Use of Probability for Dealing with Uncertainty in Artificial Intelligence

  • Carlotta Piscopo
  • Mauro Birattari


In artificial intelligence (AI), a number of criticisms were raised against the use of probability for dealing with uncertainty. All these criticisms, except what in this article we call the non-adequacy claim, have been eventually confuted. The non-adequacy claim is an exception because, unlike the other criticisms, it is exquisitely philosophical and, possibly for this reason, it was not discussed in the technical literature. A lack of clarity and understanding of this claim had a major impact on AI. Indeed, mostly leaning on this claim, some scientists developed an alternative research direction and, as a result, the AI community split in two schools: a probabilistic and an alternative one. In this article, we argue that the non-adequacy claim has a strongly metaphysical character and, as such, should not be accepted as a conclusive argument against the adequacy of probability.


Artificial intelligence Probability Alternative approaches Randomness Uncertainty 



Carlotta Piscopo acknowledges the support of a Training Site fellowship funded by the Improving Human Potential (IHP) programme of the Commission of the European Community, Grant HPMT-CT-2000-00032. Mauro Birattari acknowledges support from the fund for scientific research F.R.S.—FNRS of Belgium’s French Community, of which he is a Research Associate.


  1. Bellman, R. E., & Zadeh, L. (1970). Decision making in a fuzzy environment. Management Science, 17(4), 141–164.MathSciNetCrossRefGoogle Scholar
  2. Billingsley, P. (1986). Probability and measure (2nd ed.). New York, NY, USA: Wiley.MATHGoogle Scholar
  3. Blair, B. (1999). Famous people: Then and now. Lotfi Zadeh. Creator of fuzzy sets. Azerbaijan International, December. Interview with Lotfi Zadeh.Google Scholar
  4. Brooks, R. (1990). Elephants don’t play chess. Robotics and Autonomous Systems, 6, 3–15.CrossRefGoogle Scholar
  5. Brooks, R. A. (1991). Intelligence without reason. In Proceedings of the International Joint Conference on Artificial Intelligence, pp. 569–595, Morgan Kaufmann Publisher, San Mateo, California.Google Scholar
  6. Buchanan, B., & Feigenbaum, E. (1978). Dendral and meta-dendral: Their applications dimension. Artificial Intelligence, 11(1, 2), 5–24.CrossRefGoogle Scholar
  7. Buchanan, B. G., & Shortliffe, E. H. (Eds.). (1984). Rule-based expert systems. The MYCIN Experiments of the Stanford Heuristic Programming Project. Reading, MA, USA: Addison-Wesley.Google Scholar
  8. Cheeseman, P. (1985). In defense of probability. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pp. 1002–1009, Morgan Kaufmann Publisher, San Mateo, CA, USA.Google Scholar
  9. Dempster, A. P. (1967). Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38, 325–339.CrossRefMathSciNetMATHGoogle Scholar
  10. Dubois, D., & Prade, H. (1987). Théorie des Possibilités (2nd ed.). Paris, France: Masson.Google Scholar
  11. Dubois, D., & Prade, H. (1997). Bayesian conditioning in possibility theory. Fuzzy Sets and Systems, 92, 223–240.CrossRefMathSciNetMATHGoogle Scholar
  12. Dubois, D., & Prade, H. (1999). Editorial. Fuzzy Sets and Systems, 101(1), 1–3.CrossRefGoogle Scholar
  13. Duda, R. O., Gaschnig, J., & Hart, P. E. (1979). Model design in the prospector consultant system for mineral exploration. In D. Michie (Ed.), Expert systems in the microelectronic age (pp. 153–167). Edinburgh, UK: Edinburgh University Press.Google Scholar
  14. Eagle, A. (2005). Randomness is unpredictability. The British Journal for the Philosophy of Science, 56(4), 749–790.CrossRefMathSciNetMATHGoogle Scholar
  15. Garvey, T. D., Lowrance, J. D., & Fischler, M. A. (1981). An inference technique for integrating knowledge from disparate sources. In Proceedings of the Seventh International Joint Conference on Artificial Intelligence, pp. 319–325, Morgan Kaufmann Publisher, San Mateo, CA, USA.Google Scholar
  16. Hacking, I. (1975). The emergence of probability. Cambridge, UK: Cambridge University Press.MATHGoogle Scholar
  17. Kolmogorov, A. N. (1963). On tables of random numbers. Sankhya. The Indian Journal of Statistics, A, 25, 369–376.MathSciNetMATHGoogle Scholar
  18. Marsaglia, G. (1995). Die Hard: A battery of tests for random number generators.∼geo/diehard.html.
  19. Martin-Löf, P. (1966). The definition of random sequences. Information and Control, 9, 602–619.CrossRefMathSciNetGoogle Scholar
  20. McCarthy, J., & Hayes, P. J. (1969). Some philosophical problems from the standpoint of artificial intelligence. In B. Meltzer & D. Michie (Eds.), Machine intelligence 4 (pp. 463–502). Edinburgh, UK: Edinburgh University Press.Google Scholar
  21. Newell, A., Shaw, J. C., & Simon, H. (1957). Empirical explorations with the logic theory machine: A case study in heuristics. In Proceedings of the Western Joint Computer Conference 15, pp. 218–239.Google Scholar
  22. Newell, A., Shaw, J. C., & Simon, H. (1958). Chess playing programs and the problem of complexity. IBM Journal of Research and Development, 2, 320–335.MathSciNetCrossRefGoogle Scholar
  23. Nikravesh, M. (2007). Evolution of fuzzy logic: From intelligent systems and computation to human mind. In M. Nikravesh, J. Kacprzyk, & L. Zadeh (Eds.), Forging new frontiers: Fuzzy Pioneers I (Vol. 217, pp. 37–53). Berlin, Germany: Springer.CrossRefGoogle Scholar
  24. Nilsson, N. J. (1984). Shakey the robot. Technical Report Technical Note 323, SRI AI Center, Menlo Park, CA, USA.Google Scholar
  25. Pearl, J. (1988). Probabilistic reasoning in intelligent systems. Networks of plausible inference. San Mateo, CA, USA: Morgan Kaufmann.Google Scholar
  26. Popper, K. (1935). Logik der Forschung. Available as: The Logic of Scientific Discovery, London, United Kingdom: Routledge. 1999.Google Scholar
  27. Shafer, G. (1976). A mathematical theory of evidence. Princeton, NJ, USA: Princeton University Press.MATHGoogle Scholar
  28. Shafer, G. (1978). Non additive probabilities in the work of Bernoulli and Lambert. Archive for History of Exact sciences, 19, 309–370.CrossRefMathSciNetMATHGoogle Scholar
  29. Shafer, G., & Pearl, J. (Eds.). (1990). Uncertain reasoning. San Mateo, CA, USA: Morgan Kaufmann Publisher.MATHGoogle Scholar
  30. Shortliffe, E. H. (1980). Consultation systems for physicians: The role of artificial intelligence techniques. In Proceedings of the Third National Conference of the Canadian Society for Computational Studies of Intelligence, pp. 1–11.Google Scholar
  31. Smets, P., & Kennes, R. (1994). The transferable belief model. Artificial Intelligence, 66(2), 191–234.CrossRefMathSciNetMATHGoogle Scholar
  32. Solo, A. M. G., & Gupta, M. (2007). Uncertainty in computational perception and cognition. In M. Nikravesh, J. Kacprzyk, & L. Zadeh (Eds.), Forging new frontiers: Fuzzy Pioneers I, (vol. 217, pp. 251–266). Berlin, Germany: Springer.CrossRefGoogle Scholar
  33. Sutton, R. S., & Barto, A. G. (1998). Reinforcement learning. An introduction. Cambridge, MA, USA: MIT Press.Google Scholar
  34. Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, 1124–1131.CrossRefGoogle Scholar
  35. Walley, P. (1991). Statistical reasoning with imprecise probabilities. New York, NY, USA: Chapman and Hall.MATHGoogle Scholar
  36. Walley, P. (1996). Measures of uncertainty in expert systems. Artificial Intelligence, 83(1), 1–58.CrossRefMathSciNetGoogle Scholar
  37. Walley, P. (2000). Toward a unified theory of imprecise probability. International Journal of Approximate Reasoning, 24, 125–148.CrossRefMathSciNetMATHGoogle Scholar
  38. Watkins, C. J. C. H. (1989). Learning from Delayed Rewards. PhD thesis, King’s College, United Kingdom: Cambridge.Google Scholar
  39. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.CrossRefMathSciNetMATHGoogle Scholar
  40. Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1(1), 3–28.CrossRefMathSciNetMATHGoogle Scholar
  41. Zadeh, L. A. (1981). Possibility theory and soft data analysis. In L. Cobb & R. M. Thrall (Eds.), Mathematical frontiers of the social and policy sciences (pp. 69–129). Boulder, CO, USA: Westview Press.Google Scholar
  42. Zadeh, L. A. (2005). Toward a generalized theory of uncertainty (GTU)—an outline. Information Sciences, 172, 1–40.CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.IRIDIA, CoDEUniversité Libre de BruxellesBrusselsBelgium

Personalised recommendations