Conditional indifference and conditional preservation

TL;DR

This paper introduces a new approach to belief revision focusing on conditionals, emphasizing a principle of conditional preservation that applies across qualitative and quantitative frameworks.

Contribution

It axiomatizes a principle of conditional preservation as an indifference property, unifying various approaches to belief revision involving conditionals.

Findings

The principle covers existing approaches to conditional preservation.

It applies to both qualitative and quantitative belief revision frameworks.

Provides a formal axiomatization of conditional preservation in belief revision.

Abstract

The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we present a new approach to conditionals, capturing particularly well their dynamic part as revision policies. We thoroughly axiomatize a principle of conditional preservation as an indifference property with respect to conditional structures of worlds. This principle is developed in a semi-quantitative setting, so as to reveal its fundamental meaning for belief revision in quantitative as well as in qualitative frameworks. In fact, it is shown to cover other proposed approaches to conditional preservation.