# A Conditional Perspective on the Logic of Iterated Belief Contraction

arXiv: https://arxiv.org/abs/2202.03196 · HTML: https://mlsanity.com/paper/2202.03196/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 87 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 5 of 5)

- [Decrement Operators in Belief Change](https://mlsanity.com/paper/1905.08347/) (2019)
- [A Conditional Perspective for Iterated Belief Contraction](https://mlsanity.com/paper/1911.08833/) (2019)
- [Extending the Harper Identity to Iterated Belief Change](https://mlsanity.com/paper/1604.05419/) (2016)
- [Elementary Iterated Revision and the Levi Identity](https://mlsanity.com/paper/1907.01224/) (2019)
- [A General Katsuno-Mendelzon-Style Characterization of AGM Belief Base Revision for Arbitrary Monotonic Logics](https://mlsanity.com/paper/2104.14512/) (2021)

## Built on by (most cited first, 2 of 2)

- [Representing states in iterated belief revision](https://mlsanity.com/paper/2305.09200/) (2023)
- [Can we forget how we learned? Doxastic redundancy in iterated belief revision](https://mlsanity.com/paper/2402.15445/) (2024)

## Abstract (arXiv)

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  α -equivalence for formulating some of the new postulates.