Who is Afraid of Minimal Revision?

TL;DR

This paper explores the capabilities and limitations of minimal revision in belief revision theory, showing it can learn in certain finite scenarios but struggles with more complex or erroneous information.

Contribution

It characterizes the learning power of minimal revision, compares it with other methods, and analyzes conditions under which it successfully learns.

Findings

Minimal revision can learn finitely identifiable problems.

It can learn from positive and negative data with finite possibilities.

Not all results hold when learning from erroneous information.

Abstract

The principle of minimal change in belief revision theory requires that, when accepting new information, one keeps one's belief state as close to the initial belief state as possible. This is precisely what the method known as minimal revision does. However, unlike less conservative belief revision methods, minimal revision falls short in learning power: It cannot learn everything that can be learned by other learning methods. We begin by showing that, despite this limitation, minimal revision is still a successful learning method in a wide range of situations. Firstly, it can learn any problem that is finitely identifiable. Secondly, it can learn with positive and negative data, as long as one considers finitely many possibilities. We then characterize the prior plausibility assignments (over finitely many possibilities) that enable one to learn via minimal revision, and do the same for conditioning and lexicographic upgrade. Finally, we show that not all of our results still hold when learning from possibly erroneous information.