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Structural and Probabilistic Knowledge for Abductive Reasoning
March 1993 (vol. 15 no. 3)
pp. 233-245

Different ways of representing probabilistic relationships among the attributes of a domain ar examined, and it is shown that the nature of domain relationships used in a representation affects the types of reasoning objectives that can be achieved. Two well-known formalisms for representing the probabilistic among attributes of a domain. These are the dependence tree formalism presented by C.K. Chow and C.N. Liu (1968) and the Bayesian networks methodology presented by J. Pearl (1986). An example is used to illustrate the nature of the relationships and the difference in the types of reasoning performed by these two representations. An abductive type of reasoning objective that requires use of the known qualitative relationships of the domain is demonstrated. A suitable way to represent such qualitative relationships along with the probabilistic knowledge is given, and how an explanation for a set of observed events may be constituted is discussed. An algorithm for learning the qualitative relationships from empirical data using an algorithm based on the minimization of conditional entropy is presented.

[1] R. Bhatnagar, "Construction of preferred causal hypotheses for reasoning with uncertain knowledge," Ph.D. dissertation, Comput. Sci. Dept., Univ. Maryland, College Park, 1989.
[2] R. Bhatnagar and L. N. Kanal, "Hypothesizing causal models for reasoning." Tech. Rep. CIS-TR-91-4. Univ. of Cincinnati, Cincinnati, OH, 1991.
[3] E. Charniak and S. E. Shimony, "Probabilistic semantics for cost based abduction," inProc. 8th Nat. Conf. Artificial Intell.(Boston), 1990, pp 106-111.
[4] C. K. Chow and C. N. Liu, "Approximating discrete probability distributions with dependence trees,"IEEE Trans. Inform. Theory, vol. IT-14, no. 3. May 1968.
[5] G. F. Cooper and E. Herskovits, "A Bayesian method for constructing Bayesian belief networks from databases," inProc. Seventh Conf. Uncertainty Artificial Intell., 1991, pp. 86-94.
[6] J. de Kleer and B. C. Williams, "Diagnosis with behavioral modes," inProc. IJCAI, 1989, pp. 1324-1330.
[7] R. M. Fung and S. L. Crawford, "Constructor: A system for induction of probabilistic models," inProc. AAAI, 1990, pp. 762-769.
[8] E. Herskovits and G. Cooper, "An entropy-driven system for construction of probabilistic expert systems from databases," inUncertainty in Artificial Intelligence 6(P. P. Bonissone, M. Henrion, L. N. Kanal, and J. F. Lemmer, Eds.). Amsterdam: North Holland, 1991, pp. 117-125.
[9] S. L. Lauritzen and D. J. Spiegelhalter, "Local computations with probabilities on graphical structures and their application to expert systems,"J. Royal Stat. Soc. Series B, vol. 50, no. 2, pp. 157-224, 1988.
[10] R. E. Neapolitan,Probabilistic Reasoning in Expert Systems. New York: Wiley, 1990.
[11] J. Pearl, "Fusion, propagation, and structuring in belief networks,"Artif. Intell., vol. 29, no. 3, pp. 241-288, 1986.
[12] J. Pearl, "Fusion, propagation, and structuring in belief networks,"Artif. Intell., vol. 33, pp. 173-215, 1987.
[13] J. Pearl and T. S. Verma, "A theory of inferred causation," inPrinciples Knowledge Represent. Rea.: Proc. Second Int. Conf., Apr. 1991.
[14] C. S. Peirce,The Philosophy of Peirce--Selected Writings(J. Buchler, Ed.). New York: Harcourt, 1940.
[15] Y. Peng and J. A. Reggia, "Diagnostic problem solving with causal chaining,"Inc. J. Intell. Syst., vol. II, pp. 265-302, 1987.
[16] D. Poole, "A logical framework for default reasoning,"Artificial Intell., vol. 36, pp. 27-47, 1988.
[17] D. Poole and G. M. Provan, "What is most likely diagnosis?" inUncertainty in Artificial Intelligence 6(P. P. Bonissone, M. Henrion, L. N. Kanal, and J. F. Lemmer, Ed.). Amsterdam: North Holland, 1991.
[18] D. Poole, "Representing Bayesian networks within probabilistic Horn abduction," inProc. Seventh Conf. Uncertainty Artificial Intell.(Los Angeles, CA), 1991, pp. 271-278.
[19] J. R. Quinlan, "Induction of decision trees,"Machine Learning, vol. 1, no. 1, pp. 81-106, 1986.

Index Terms:
structural knowledge; qualitative relationships learning; probabilistic knowledge; abductive reasoning; conditional entropy; explanation; inference mechanisms; knowledge engineering; learning (artificial intelligence); probabilistic logic
R. Bhatnagar, L.N. Kanal, "Structural and Probabilistic Knowledge for Abductive Reasoning," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 3, pp. 233-245, March 1993, doi:10.1109/34.204905
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