Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Reasoning with BKBs – Algorithms and Complexity

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

Bayesian Knowledge Bases (BKB) are a rule-based probabilistic model that extends the well-known Bayes Networks (BN), by naturally allowing for context-specific independence and for cycles in the directed graph. We present a semantics for BKBs that facilitate handling of marginal probabilities, as well as finding most probable explanations.

Complexity of reasoning with BKBs is NP hard, as for Bayes networks, but in addition, deciding consistency is also NP-hard. In special cases that problem does not occur. Computation of marginal probabilities in BKBs is another hard problem, hence approximation algorithms are necessary – stochastic sampling being a commonly used scheme. Good performance requires importance sampling, a method that works for BKBs with cycles is developed.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. F. Bacchus, Representing and Reasoning with Probabilistic Knowledge: A Logical Approach to Probabilities (MIT Press, 1990).

  2. C. Boutilier, N. Friedman, M. Goldszmidt and D. Koller, Context-specific independence in Bayesian networks, in: Uncertainty in Artificial Intelligence, Proceedings of the 12th Conference (Morgan Kaufmann, August 1996) pp. 115–123.

  3. G.F. Cooper, The computational complexity of probabilistic inference using Bayesian belief networks, Artificial Intelligence 44 (1990) 393–405.

    Google Scholar 

  4. P. Dagum and M. Luby, Approximating probabilistic inference in Bayesian belief networks is NP-hard, Artificial Intelligence 60(1) (March 1993) 141–153.

    Google Scholar 

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

    Google Scholar 

  6. C. Domshlak, D. Gershkovich, E. Gudes, N. Liusternik, A. Meisels, T. Rosen and S.E. Shimony, FlexiMine-a flexible platform for KDD research and application construction, in: KDD-98, Proceedings of the Fourth International Conference on Knowledge Discovery in Databases (1998) pp. 184–188.

  7. W.F. Dowling and J.H. Gallier, Linear-time algorithms for testing the satisfiability of propositional Horn formulae, Journal of Logic Programming 3 (1984) 267–284.

    Google Scholar 

  8. D. Heckerman, Probabilistic Similarity Networks (MIT Press, 1991).

  9. M. Henrion, Propagating uncertainty in Bayesian networks by probabilistic logic sampling, in: Proceedings Uncertainty in Artificial Intelligence 4 (1988) pp. 149–163.

    Google Scholar 

  10. G. Johnson, Jr. and E. Santos, Jr., Generalizing knowledge representation rules for acquiring and validating uncertain knowledge, in: Proceedings of the 13th International Florida Artificial Intelligence Research Society Conference (May 2000) pp. 186–190.

  11. N.J. Nilsson, Probabilistic logic, Artificial Intelligence 28 (1986) 71–87.

    Google Scholar 

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

    Google Scholar 

  13. D. Poole, Probabilistic Horn abduction and Bayesian networks, Artificial Intelligence 64(1) (1993) 81–129.

    Google Scholar 

  14. T. Rosen and S.E. Shimony, BKBs-semantics, characteristics, and inference, Technical Report FC-99-07, Ben-Gurion University (1999).

  15. E. Santos, Jr. and E.S. Santos, A framework for building knowledge-bases under uncertainty, Journal of Experimental and Theoretical Artificial Intelligence 11 (1999) 265–286.

    Google Scholar 

  16. E.S. Santos and E.Santos, Jr., Reasoning with uncertainty in a knowledge-based system, in: Proceedings of the International Symposium on Multiple-Valued Logic (1987) pp. 75–81.

  17. E. Santos Jr., A linear constraint satisfaction approach to cost-based abduction, Artificial Intelligence 65(1) (1994) 1–27.

    Google Scholar 

  18. G.A. Shafer, Mathematical Theory of Evidence (Princeton University Press, 1979).

  19. S.E. Shimony, The role of relevance in explanation I: Irrelevance as statistical independence, International Journal of Approximate Reasoning 8(4) (June 1993) 281–324.

    Google Scholar 

  20. S.E. Shimony, Finding MAPs for belief networks is NP-hard, Artificial Intelligence 68(2) (August 1994) 399–410.

    Google Scholar 

  21. S.E. Shimony, The role of relevance in explanation II: Disjunctive assignments and approximate independence, International Journal of Approximate Reasoning 13(1) (July 1995) 27–60.

    Google Scholar 

  22. S.E. Shimony, E. Santos, Jr. and T. Rosen, Independence semantics for BKBs, in: Proceedings of the 13th International Florida Artificial Intelligence Research Society Conference (May 2000) pp. 308–312.

  23. E.H. Shortliffe and B.G. Buchanan, A model of inexact reasoning in medicine, Mathematical Biosciences 23 (1975) 351–379.

    Google Scholar 

  24. P. Spirtes, C. Glymour and R. Scheines, Causation, Prediction, and Search (Springer, 1993).

  25. P. Thagard, Explanatory coherence, Behavioral and Brain Sciences 12 (1989) 435–502.

    Google Scholar 

  26. L.A. Zadeh, The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems 11 (1983) 199–227.

    Google Scholar 

  27. N.L. Zhang and D. Poole, Intercausal independence and heterogeneous factorization, in: Uncertainty in AI, Proceedings of the Tenth Conference (July 1994) pp. 606–614.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Ben Gurion University, P.O. Box 653, Beer-Sheva, 84105, Israel

    Tzachi Rosen & Solomon Eyal Shimony

  2. Department of Computer Science and Engineering, University of Connecticut at Storrs, CT, 06269, USA

    Eugene Santos Jr.

Authors
  1. Tzachi Rosen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Solomon Eyal Shimony
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eugene Santos Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rosen, T., Shimony, S.E. & Santos, E. Reasoning with BKBs – Algorithms and Complexity. Annals of Mathematics and Artificial Intelligence 40, 403–425 (2004). https://doi.org/10.1023/B:AMAI.0000012874.65239.b0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:AMAI.0000012874.65239.b0

Search

Navigation