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<p>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.</p>
structural knowledge; qualitative relationships learning; probabilistic knowledge; abductive reasoning; conditional entropy; explanation; inference mechanisms; knowledge engineering; learning (artificial intelligence); probabilistic logic

R. Bhatnagar and L. Kanal, "Structural and Probabilistic Knowledge for Abductive Reasoning," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 15, no. , pp. 233-245, 1993.
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