Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Foundations of Information and Knowledge Systems

FoIKS 2004: Foundations of Information and Knowledge Systems pp 196–212Cite as

A New Approach to Belief Modeling

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2942))

Abstract

It has been shown that, despite the differences in approach and interpretation, all belief function based models without the so-called dynamic component lead essentially to mathematically equivalent theories – at least in the finite case. In this paper, we first argue that at the logical level these models seem to share a common formal framework and various interpretations just come at the epistemic level. We then introduce a framework for belief modeling formally based on Dempster’s structure with adopting Smets’ view of the origin of beliefs. It is shown that the proposed model is more general than previous models, and may provide a suitable unified framework for belief modeling.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. DeGroot, M.H.: Optimal Statistical Decisions. McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  2. Dempster, A.P.: Upper and lower probabilities induced by a multi-valued mapping. Annals of Mathematics and Statistics 38, 325–339 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dempster, A.P.: A generalization of Bayesian inference. Journal of the Royal Statistical Society, Series B 30, 205–247 (1968)

    MathSciNet  Google Scholar 

  4. Elouedi, Z., Mellouli, K., Smets, P.: Belief decision trees: theoretical foundations. International Journal of Approximate Reasoning 28, 91–124 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Fagin, R., Halpern, J.Y.: Uncertainty, belief, and probability. Computational Intelligence 7, 160–173 (1991)

    Article  Google Scholar 

  6. Fagin, R., Halpern, J.Y.: A new approach to updating beliefs. In: Bonissone, P.P., et al. (eds.) Uncertainty in Artificial Intelligence, vol. 6, pp. 347–374 (1991)

    Google Scholar 

  7. Gebhardt, J., Kruse, R.: The context model: An integrating view of vagueness and uncertainty. International Journal of Approximate Reasoning 9, 283–314 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Halmos, P.: Measure Theory. Van Nostrand, New York (1950)

    MATH  Google Scholar 

  9. Halpern, J.Y., Fagin, R.: Two views of belief: belief as generalized probability and belief as evidence. Artificial Intelligence 54, 275–317 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Halpern, J.Y., Rabin, M.O.: A logic to reason about likelihood. Artificial Intelligence 32(3), 379–405 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  11. Huynh, V.N., Ryoke, M., Nakamori, Y., Ho, T.B.: Fuzziness and uncertainty within the framework of context model. In: De Baets, B., Kaynak, O., Bilgiç, T. (eds.) IFSA 2003. LNCS, vol. 2715, pp. 219–228. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  12. Kohlas, J.: Support and plausibility functions induced by filter-valued mappings. International Journal of General Systems 21(4), 343–363 (1993)

    Article  MATH  Google Scholar 

  13. Kohlas, J., Monney, P.A.: Representation of evidence by hints. In: Yager, R.R., et al. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 473–492. John Wiley, New York (1994)

    Google Scholar 

  14. Kohlas, J., Monney, P.A.: A Mathematical Theory of Hints: An Approach to Dempster-Shafer Theory of Evidence. Lecture Notes in Economics and Mathematical Systems, vol. 425. Springer, Heidelberg (1995)

    MATH  Google Scholar 

  15. Murai, T., Miyakoshi, M., Shimbo, M.: Soundness and completeness theorems between the Dempster-Shafer theory and logic of belief. In: Proceedings of the Third EEE Conference on Fuzzy Systems, Orlando, Florida, June 1994, pp. 855–858 (1994)

    Google Scholar 

  16. Nilsson, N.: Probabilistic logic. Artificial Intelligence 28, 71–87 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  17. Nguyen, H.T.: On random sets and belief functions. Journal of Mathematical Analysis and Applications 65, 531–542 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  18. Pearl, J.: Reasoning with belief functions: an analysis of compatibility. International Journal of Approximate Reasoning 4, 363–390 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  19. Rasiowa, H.: An Algebraic Approach to Non-classical Logic. North-Holland, Amsterdam (1974)

    Google Scholar 

  20. Resconi, G., Klir, G., Clair, U.S.: Hierarchically uncertainty metatheory based upon modal logic. International Journal of General Systems 21, 23–50 (1992)

    Article  MATH  Google Scholar 

  21. Ruspini, E.H.: The logical foundations of evidential reasoning, Technical Report 408, AI Center, SRI International, Menlo Park, California (1986)

    Google Scholar 

  22. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  23. Shafer, G.: Allocations of probability. Annals of Probability 7(5), 827–839 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  24. Smets, P.: Belief functions. In: Smets, P., et al. (eds.) Non Standard Logics for Automated Reasoning, pp. 253–286. Academic Press, London (1988)

    Google Scholar 

  25. Smets, P.: The combination of evidence in the transferable belief model. IEEE Transactions on Patter Analysis and Machine Intelligence 12(5), 447–458 (1990)

    Article  Google Scholar 

  26. Smets, P.: Resolving misunderstandings about belief functions: a response to the many criticisms raised by J. Pearl. International Journal of Approximate Reasoning 6, 321–344 (1992)

    Article  MATH  Google Scholar 

  27. Smets, P.: Quantifying beliefs by belief functions: An axiomatic justification. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence, pp. 598–603. Morgan Kaufmann, San Mateo (1993)

    Google Scholar 

  28. Smets, P., Kennes, R.: The transferable belief model. Artificial Intelligence 66, 191–234 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  29. Smets, P.: What is Dempster–Shafer’s model. In: Yager, R.R., et al. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 5–34. John Wiley, New York (1994)

    Google Scholar 

  30. Smets, P.: The normative representation of quantified beliefs by belief functions. Artificial Intelligence 92, 229–242 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  31. Smets, P., Kruse, R.: The transferable belief model for belief representation. In: Motro, A., Smets, P. (eds.) Uncertainty Management in Information Systems: From Needs to Solutions, pp. 343–368. Kluwer, Boston (1997)

    Google Scholar 

  32. Zadeh, L.A.: Fuzzy logics and approximate reasoning. Synthese 30, 407–428 (1975)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Knowledge Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa, 923-1292, Japan

    V. N. Huynh, Y. Nakamori & T. B. Ho

  2. Graduate School of Engineering, Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, 060-8628, Japan

    T. Murai

Authors
  1. V. N. Huynh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Nakamori
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Murai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. B. Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    Dietmar Seipel

  2. Department of Information Systems, Massey University, Information Science Research Centre, PO Box 756, Wellington, New Zealand

    José María Turull-Torres

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Huynh, V.N., Nakamori, Y., Murai, T., Ho, T.B. (2004). A New Approach to Belief Modeling. In: Seipel, D., Turull-Torres, J.M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2004. Lecture Notes in Computer Science, vol 2942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24627-5_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24627-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20965-2

  • Online ISBN: 978-3-540-24627-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation