STRUCTURAL AND PROBABILISTIC KNOWLEDGE FOR ABDUCTIVE REASONING

We examine different ways of representing probabilistic relationships among the attributes of a domain and show that the nature of domain relationships used in a representation affects the types of reasoning objectives that can be achieved. We review two well-known formalisms for representing the probabilistic relationships among attributes of a domain. These are the dependence tree formalism presented by Chow and Liu and the Bayesian networks methodology presented by Pearl. We use an example to illustrate the nature of the relationships and the difference in the types of reasoning performed by these two representations. We then demonstrate an abductive type of reasoning objective that requires use of the known qualitative relationships of the domain. We demonstrate a suitable way to represent such qualitative relationships along with the probabilistic knowledge, and we discuss how an explanation for a set of observed events may be constituted. We also present an algorithm for learning the qualitative relationships from empirical data using an algorithm based on the minimization of conditional entropy.