Abstract
A Bayesian network is a knowledge representation technique for use in expert system development. The probabilistic knowledge encoded in a Bayesian network is a set of composite hypotheses expressed over the permutation of a set of variables (propositions). Ordering these composite hypotheses according to their a posteriori probabilities can be exponentially hard. This paper presents a qualitative reasoning approach which takes advantage of certain types of topological structures and probability distributions of a Bayesian network to derive the partial ordering of composite hypotheses. Such an approach offers an attractive alternative to reduce the computational complexity of deriving a partial ordering in which consistency is guaranteed.
Similar content being viewed by others
References
J. Pearl, Fusion, propagation, and structuring in Bayesian networks, Art. Int. 28 (1986) 241–288.
J. Pearl, Distributed revision of composite beliefs, Art. Int. 33 (1987) 173–215.
B.K. Sy, An AI-based CAD/CAM approach to assess design methodology of a user-specific nonvocal communication device,Proc. 15th Northeast Bioengineering Conf., Boston (March 1989).
G.F. Cooper, A diagnostic method that uses causal knowledge and linear programming in the application of Bayes' formula, Comp. Meth. Programs Biomed. 22 (1986) 223–237.
G.F. Cooper, Probabilistic inference using belief networks in NP-hard, Knowledge Systems Laboratory, Stanford University, Memo KSL-87-27 (May 1987; revised Aug. 1987).
A. Rege and A.M. Agogino, Topological framework for representing and solving probabilistic inference problems in expert systems, IEEE Trans. Systems, Man, and Cybernetics SMC-18 (1988) 402–414.
M.F. Sipser, We still don't know if P=NP,MIT Computer Science Research Symp. (Oct. 1988).
B.K. Sy, Qualitative reasoning of quantitative uncertainty in Bayesian networks,Proc. Int. Computer Science Conf., Hong Kong (Dec. 1988).
B.K. Sy, Qualitative reasoning of Bayesian belief using meta-knowledge,Proc. Int. Joint Conf. of AI, Detroit, MI (Aug. 1989).
K.D. Forbus, Qualitative process theory, Art. Int. 24 (1984) 85–168.
M.P. Wellman, Qualitative probabilistic networks for planning under certainty, in:Uncertainty in Artificial Intelligence, Vol. 2, ed. J.F. Lemmer (North-Holland, 1987).
M.P. Wellman, Probabilistic semantics for qualitative influences,Proc. National Conf. on Artificial Intelligence (AAAI, 1987) pp. 660–664.
A. Gill,Applied Algebra for the Computer Science (Prentice-Hall, 1976) pp. 142–47.
A.M. Yaglom and I.M. Yaglom,Probability and Information (D. Reidel, 1983) appendix I.
B. Kuipers, Commonsense reasoning about causality: deriving behavior from structure, Art. Int. 24 (1984) 169–203.
M. Henrion, An introduction to algorithm for inference in belief nets,Uncertainty in Artificial Intelligence 5 (MIPR 10), eds. M. Henrion, R. Shachter, L. Kanal, and J. Lemmer (Elsevier Science/North-Holland, 1990).
Author information
Authors and Affiliations
Additional information
This work is supported in part by a grant to Queens College from the General Research Branch, National Institute of Health under grant No. RR-07064.
Rights and permissions
About this article
Cite this article
Sy, B.K. Reasoning composite beliefs using a qualitative approach. Ann Math Artif Intell 4, 1–23 (1991). https://doi.org/10.1007/BF01531171
Issue Date:
DOI: https://doi.org/10.1007/BF01531171