Learning, Bayesian Probability, Graphical Models, and Abduction 1

In this chapter I review Bayesian statistics as used for induction and relate it to logic-based abduction. Much reasoning under uncertainty , including induction, is based on Bayes' rule. Bayes' rule is interesting precisely because it provides a mechanism for abduction. I review work of Buntine that argues that much of the work on Bayesian learning can be best viewed in terms of graphical models such as Bayesian networks, and review previous work of Poole that relates Bayesian networks to logic-based abduction. This lets us see how much of the work on induction can be viewed in terms of logic-based abduction. I then explore what this means for extending logic-based abduction to richer representations, such as learning decision trees with probabilities at the leaves. Much of this paper is tutorial in nature ; both the probabilistic and logic-based notions of abduction and induction are introduced and motivated.