Skip to main content

Probabilistic default logic based on irrelevance and relevance assumptions

  • Accepted Papers
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1244))

Abstract

This paper embeds default logic into an extension of Adams' probability logic, called the system P + DP. Default reasoning is furnished with two mechanisms: one generates (ir)relevance assumptions, and the other propagates lower probability bounds. Together both mechanisms make default reasoning probabilistically reliable. There is an exact correspondence between Poole-extensions and P + DP-extensions. The procedure for P + DP-entailment is comparable in complexity with Poole's procedure.

I am indebted to Ernest Adams for various help.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. W. Adams. The Logic of Conditionals. Reidel, Dordrecht, 1975.

    Google Scholar 

  2. E. W. Adams. On the logic of high probability. Journal of Philosophical Logic, 15:255–279, 1986.

    Google Scholar 

  3. F. Bacchus. Representing and Reasoning with Probabilistic Knowledge. MIT Press, Cambridge, Mass., 1990.

    Google Scholar 

  4. G. Brewka. Nonmonotonic Reasoning. The Logic of Commonsense. Cambridge University Press, 1991.

    Google Scholar 

  5. R. Carnap. Logical Foundations of Probability. University of Chicago Press, second edition, 1962.

    Google Scholar 

  6. J.P. Delgrande. An approach to default reaoning based on a first-order conditional logic: revised report. Artificial Intelligence, 36:63–90, 1988.

    Google Scholar 

  7. A.M. Frisch and P. Haddawy. Anytime deduction for probabilistic logic. Artificial Intelligence, 69:93–122, 1994.

    Google Scholar 

  8. H. Geffner and J. Pearl. A framework for reasoning with defaults. In H.E. Kyburg et al., editors, Knowledge Representation and Defeasible Reasoning, pages 69–87. Kluwer, The Netherlands, 1990.

    Google Scholar 

  9. M. Goldszmidt and J. Pearl. Qualitative probabilities for default reasoning, belief revision and causal modeling. Artificial Intelligence, 84:57–112, 1996.

    Google Scholar 

  10. D. Lehmann and M. Magidor. What does a conditional knowledge base entail? Artificial Intelligence, 55:1–60, 1992.

    Google Scholar 

  11. A. Y. Levy and Y. Sagiv. Exploiting irrelevance reasoning to guide problem solving. In Proceedings IJCAI-93, pages 138–144, Santa Mateo, 1993.

    Google Scholar 

  12. J. Pearl. Fusion, propagation, and structuring in belief networks. Artificial Intelligence, 29:241–288, 1986.

    Google Scholar 

  13. J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, CA, 1988.

    Google Scholar 

  14. D. Poole. A logical framework for default reasoning. Artificial Intelligence, 36:27–47, 1988.

    Google Scholar 

  15. D. Poole. Compiling a default reasoning system into prolog. New Generation Computing, 9:3–38, 1991.

    Google Scholar 

  16. R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.

    Google Scholar 

  17. G. Schurz. Probabilistic justification of default reasoning. In B. Nebel and L. Dreschler-Fischer, editors, KI-94: Advances in Artificial Intelligence, pages 248–259. Springer, Berlin, 1994.

    Google Scholar 

  18. G. Schurz. Research note: an examination of Delgrande's conditional default logic. IPS preprints 1/97, University of Salzburg, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Dov M. Gabbay Rudolf Kruse Andreas Nonnengart Hans Jürgen Ohlbach

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Schurz, G. (1997). Probabilistic default logic based on irrelevance and relevance assumptions. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds) Qualitative and Quantitative Practical Reasoning. FAPR ECSQARU 1997 1997. Lecture Notes in Computer Science, vol 1244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035647

Download citation

  • DOI: https://doi.org/10.1007/BFb0035647

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63095-1

  • Online ISBN: 978-3-540-69129-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics