Non-Monotonicity in Probabilistic Reasoning

TL;DR

This paper introduces a formal approach to non-monotonic probabilistic reasoning, focusing on default inheritance and the Maximization of Conditional Independence, with applications and comparisons to Maximum Entropy.

Contribution

It formalizes non-monotonic probabilistic reasoning using MCI and Pointwise Circumscription, highlighting its practical relevance and differences from Maximum Entropy.

Findings

Identifies non-monotonic probabilistic reasoning akin to default inheritance.

Formulates reasoning using Maximization of Conditional Independence (MCI).

Compares MCI with Maximum Entropy and discusses open questions.

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