Advertisement

On the relations between incidence calculus and ATMS

  • Weiru Liu
  • Alan Bundy
  • Dave Robertson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 747)

Abstract

This paper discusses the relationship between incidence calculus and the ATMS. It shows that managing labels for statements in an ATMS is similar to producing the incidence sets of these statements in incidence calculus. We will prove that a probabilistic ATMS can be implemented using incidence calculus. In this way, we can not only produce labels for all nodes in the system automatically, but also calculate the probability of any of such nodes in it. The reasoning results in incidence calculus can provide justifications for an ATMS automatically.

Keywords

Full Extension Belief Revision Belief Function Reasoning Pattern Probabilistic Assumption 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bundy,A., Incidence calculus: A mechanism for probabilistic, reasoning. Journal of Automated Reasoning 1:263–83, 1985.Google Scholar
  2. [2]
    Bundy,A., Incidence calculus, The Encyclopedia of AI. 663–668, 1992.Google Scholar
  3. [3]
    Bundy,A. and W. Liu, On Dempster's combination rule. Submitted to the Journal of Artificial Intelligence, 1993.Google Scholar
  4. [4]
    Correa da Silva,F. and A.Bundy (1990) On some equivalent relations between incidence calculus and Dempster-Shafer theory of evidence. Proc. of sixth conference of uncertainty in artificial intelligence, pp.378–383.Google Scholar
  5. [5]
    d'Ambrosio,B., A hybrid approach to reasoning under uncertainty, Int. J. Approx. Reasoning 2 (1988): 29–45.Google Scholar
  6. [6]
    d'Ambrosio,B., Incremental Construction and Evaluation of Defeasible Probabilistic Models, I.J.Approx. Reasoning 4 (1990): 233–260.Google Scholar
  7. [7]
    de Kleer,J., An assumption-based TMS. Artificial Intelligence 28 (1986) 127–162.Google Scholar
  8. [8]
    de Kleer,J. and B.C.Williams, Diagnosing multiple faults, Artificial Intelligence 32 (1987) 97–130.Google Scholar
  9. [9]
    Doyle,J., A truth maintenance system. Artificial Intelligence 12 (3): 231–72, 1979.Google Scholar
  10. [10]
    Dubois,D., J.Lang and H.Prade, Handling uncertain knowledge in an ATMS using possibilistic logic, ECAI-90 workshop on Truth Maintenance Systems, (1990) Stockholm, Sweden.Google Scholar
  11. [11]
    Falkenhainer, B., Towards a general purpose belief maintenance system, Proc. 2nd workshop on Uncertainty in AI. Philadelphia, 71–76, 1986.Google Scholar
  12. [12]
    Fulvio Monai,F. and T.Chehire, Possibilistic Assumption based Truth Maintenance Systems, Validation in a Data Fusion Application, Proc. of the eighth conference on uncertainty in artificial intelligence. Stanford, 83–91, 1992.Google Scholar
  13. [13]
    Laskey,K.B. and P.E. Lehner, Assumptions, Beliefs and Probabilities, Artificial Intelligence 41 (1989/90) 65–77.Google Scholar
  14. [14]
    Liu,W. and A.Bundy, Constructing probabilistic ATMS using incidence calculus. Submitted, 1993.Google Scholar
  15. [15]
    Pearl,J., Probabilistic Reasoning in Intelligence Systems: networks of plausible inference. Morgan Kaufmann Publishers, Inc., 1988.Google Scholar
  16. [16]
    Proven,G.M., An analysis of ATMS-based techniques for computing Dempster-Shafer belief functions. Proc. of the 11th International Joint Conf. on Artificial Intelligence, p:1115–1120, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Weiru Liu
    • 1
  • Alan Bundy
    • 1
  • Dave Robertson
    • 1
  1. 1.Dept. of AIUniv. of EdinburghEdinburghUK

Personalised recommendations