Non-Monotonicity in Probabilistic Reasoning

Abstract

We start by defining an approach to non-monotonic probabilistic reasoning in terms of non-monotonic categorical (true-false) reasoning. We identify a type of non-monotonic probabilistic reasoning, akin to default inheritance, that is commonly found in practice, especially in "evidential" and "Bayesian" reasoning. We formulate this in terms of the Maximization of Conditional Independence (MCI), and identify a variety of applications for this sort of default. We propose a formalization using Pointwise Circumscription. We compare MCI to Maximum Entropy, another kind of non-monotonic principle, and conclude by raising a number of open questions