Non-monotonic Reasoning and the Reversibility of Belief Change

TL;DR

This paper examines the limitations of ranked preferential models in non-monotonic reasoning, demonstrating their inability to handle iterated belief change and reversibility, thus highlighting the need for numerical belief strengths.

Contribution

It reveals that RPMs are insufficient for iterated belief change, emphasizing the necessity of incorporating numerical belief strengths for better belief revision.

Findings

RPMs cannot always reverse belief changes

Limitations of RPMs in iterated belief revision

Numerical belief strengths are needed for reversibility

Abstract

Traditional approaches to non-monotonic reasoning fail to satisfy a number of plausible axioms for belief revision and suffer from conceptual difficulties as well. Recent work on ranked preferential models (RPMs) promises to overcome some of these difficulties. Here we show that RPMs are not adequate to handle iterated belief change. Specifically, we show that RPMs do not always allow for the reversibility of belief change. This result indicates the need for numerical strengths of belief.