Possibility theory and independence

  • Luis Fariñas del Cerro
  • Andreas Herzig
Possibility Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 945)


We study the links between uncertainty and the notion of dependence. We investigate three possible definitions of dependence that are constructed from possibility measures. One of them has been proposed be Zadeh, and the two others are based on the notion of conditional possibility. We show that the latter have enough expressive power to support the whole possibility theory and that complete axiomatizations can be given.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. D. Dubois (1986), Belief Structures, Possibility Theory, Decomposable Confidence Measures on finite sets. Computer and Arti. Intell. vol 5, N∘ 5, pp 403–417.Google Scholar
  2. D. Dubois, H. Prade (1986), Possibilistic inference under matrix form. In: Fuzzy Logic in Knowledge Engeneering, ed. H. Prade and C.V. Negoita, Velag TÜV Rheinland, Köln, pp. 112–126.Google Scholar
  3. D. Dubois, H. Prade (1988), Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York.Google Scholar
  4. D. Dubois, H. Prade (1992), Belief change and Possibility Theory. In: Belief Revision, ed. P. Gärdenfors, Cambridge University Press, pp. 142–182.Google Scholar
  5. D. Dubois, L. Fariñas del Cerro, A. Herzig, H. Prade (1994), An ordinal view of independence with application to plausible reasoning. Proc. Uncertainty in AI (UAI-94), Seattle.Google Scholar
  6. L. Fariñas del Cerro, A. Herzig (1993), Interference logic = conditional logic + frame axiom. Proc. Eur. Conf. on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU-93), eds. M. Clarke, R. Kruse, S. Moral. Granada, Espagne, nov. 1993. Springer Verlag, LNCS 747, 1993, pp 105–112.Google Scholar
  7. T. Fine (1973), Theories of probability. Academic Press.Google Scholar
  8. P. Gärdenfors (1978), On the logic of relevance.Synthese 351–367.Google Scholar
  9. P. Gärdenfors (1990), Belief revision and irrelevance. PSA, Vol. 2, pp 349–356.Google Scholar
  10. E. Hisdal (1978), Conditional possibilities, independence and noninteraction. Fuzzy Sets and Systems, 1, 283–297.Google Scholar
  11. A. Kolmogorov (1956), Foundations of the Theory of Probability. Bronx, New York:Chelsea.Google Scholar
  12. J. Pearl (1988), Probabilistic reasoning in intelligent systems: Networks of plausible inference. Morgan Kauffman.Google Scholar
  13. D. Scott (1964), Measurement structures and linear inequalities. J. of Mathematical Psychology, Vol. 1, 233–247.Google Scholar
  14. K.Segerberg (1971), Qualitative probability in a modal setting. In: Proc. of the Second Scandinavian Logic Symposium (ed. J. E. Fenstad), North Holland.Google Scholar
  15. Zadeh (1978), Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, Vol. 1, pp 3–28.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Luis Fariñas del Cerro
    • 1
  • Andreas Herzig
    • 1
  1. 1.I.R.I.T.- Université Paul SabatierToulouse CedexFrance

Personalised recommendations