Non-Monotonicity in Probabilistic Reasoning
This work addresses foundational issues in probabilistic reasoning for AI and logic, but appears incremental as it builds on existing non-monotonic principles.
The paper tackles the problem of non-monotonic probabilistic reasoning by defining it in terms of categorical reasoning and proposing a formalization using Maximization of Conditional Independence (MCI) and Pointwise Circumscription, comparing it to Maximum Entropy and identifying applications.
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