A Conditional Perspective on the Logic of Iterated Belief Contraction

TL;DR

This paper explores iteration principles for belief contraction that respect conditional beliefs, providing semantic characterizations and new postulates to better understand how beliefs change over iterations.

Contribution

It introduces new semantic and syntactic principles for iterated belief contraction that incorporate conditional beliefs and proposes novel notions like $\alpha$-equivalence.

Findings

Semantic characterization theorems for contraction principles

New syntactic postulates for iterated contraction respecting conditionals

Introduction of $\alpha$-equivalence for belief change analysis

Abstract

In this article, we consider iteration principles for contraction, with the goal of identifying properties for contractions that respect conditional beliefs. Therefore, we investigate and evaluate four groups of iteration principles for contraction which consider the dynamics of conditional beliefs. For all these principles, we provide semantic characterization theorems and provide formulations by postulates which highlight how the change of beliefs and of conditional beliefs is constrained, whenever that is possible. The first group is similar to the syntactic Darwiche-Pearl postulates. As a second group, we consider semantic postulates for iteration of contraction by Chopra, Ghose, Meyer and Wong, and by Konieczny and Pino P\'erez, respectively, and we provide novel syntactic counterparts. Third, we propose a contraction analogue of the independence condition by Jin and Thielscher. For the fourth group, we consider natural and moderate contraction by Nayak. Methodically, we make use of conditionals for contractions, so-called contractionals and furthermore, we propose and employ the novel notion of $ \alpha $-equivalence for formulating some of the new postulates.