Bridging logical, comparative and graphical possibilistic representation frameworks

  • Salem Benferhat
  • Didier Dubois
  • Souhila Kaci
  • Henri Prade
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2143)

Abstract

Possibility theory offers a qualitative framework for representing uncertain knowledge or prioritized desires. A remarkable feature of this framework is the existence of three distinct compact representation formats which are all semantically equivalent to a ranking of possible worlds encoded by a possibility distribution. These formats are respectively: i) a set of weighted prepositional formulas; ii) a set of strict comparative possibility statements of the form ”p is more possible than q”, and iii) a directed acyclic graph where links are weighted by possibility degrees (either qualitative or quantitative). This paper exhibits the direct translation between these formats without resorting to a semantical (exponential) computation at the possibility distribution level. These translations are useful for fusing heterogenous information, and are necessary for taking advantages of the merits of each format at the representational or at the inferential level.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Benferhat, D. Dubois, L. Garcia, and H. Prade. Possibilistic logic bases and possibilistic graphs. In 15th Conf. on Uncertainty in Artificial Intelligence, UAI’99, 57-64, 1999.Google Scholar
  2. 2.
    S. Benferhat, D. Dubois, and H. Prade. Representing default rules in possibilistic logic. In 3rd Inter. Conf. ofPrinciples of Knowledge Repres. and Reasoning (KR’92), 673–684, 1992.Google Scholar
  3. 3.
    S. Benferhat, D. Dubois, H. Prade, and M. Williams. A practical approach to fusing and revising prioritized belief bases. In EPIA 99, LNAI 1695, 222–236, Springer Verlag,, 1999.Google Scholar
  4. 4.
    C. Boutilier, T. Deans, and S. Hanks. Decision theorie planning: Structural assumptions and computational leverage. In Journal of Artificial Intelligence Research, 11, 1–94, 1999.MATHMathSciNetGoogle Scholar
  5. 5.
    D. Dubois, J. Lang, and H. Prade. Possibilistic logic. Handbook of Logic in Artificial Intelligence and Logic Programming, 3, Oxford Univ. Press:439–513, 1994.MathSciNetGoogle Scholar
  6. 6.
    D. Dubois and H. Prade. Possibility theory: qualitative and quantitative aspects. Handbook of Defeasible Reasoning and Uncertainty Management Systems. Vol. 1, 169–226, 1998.MathSciNetGoogle Scholar
  7. 7.
    J. Gebhardt and R. Kruse. Possinfer-a software tool for possibilistic inference. In Fuzzy set Methods in Inf. Engineering. A Guided Tour ofApplications; Wiley, 1995.Google Scholar
  8. 8.
    D. Lehmann and M. Magidor. What does a conditional knowledge base entail? Artificial Intelligence, 55:1–60, 1992.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    D. Poole. Logic, knowledge representation, and bayesian decision theory. In Computational Logic-CL 2000. LNAI 1861, Springer Verlag, 70–86, 2000.Google Scholar
  10. 10.
    L. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst., 1:3–28, 1978.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Salem Benferhat
    • 1
  • Didier Dubois
    • 1
  • Souhila Kaci
    • 1
  • Henri Prade
    • 1
  1. 1.Institut de Recherche en Informatique de Toulouse (I.R.I.T.)-C.N.R.S.Université Paul SabatierToulouse Cedex 4France

Personalised recommendations