# Representing states in iterated belief revision

arXiv: https://arxiv.org/abs/2305.09200 · HTML: https://mlsanity.com/paper/2305.09200/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 59 references that are in the map.
- First posted on arXiv 16 May 2023.

## Builds on (most cited first, 6 of 6)

- [On Strengthening the Logic of Iterated Belief Revision: Proper Ordinal Interval Operators](https://mlsanity.com/paper/1807.09942/) (2018)
- [Iterated Belief Base Revision: A Dynamic Epistemic Logic Approach](https://mlsanity.com/paper/1902.06178/) (2019)
- [Iterated Belief Revision Under Resource Constraints: Logic as Geometry](https://mlsanity.com/paper/1812.08313/) (2018)
- [A Conditional Perspective on the Logic of Iterated Belief Contraction](https://mlsanity.com/paper/2202.03196/) (2022)
- [Iterated Belief Change, Computationally](https://mlsanity.com/paper/2202.08856/) (2022)
- [Dynamic Preference Logic meets Iterated Belief Change: Representation Results and Postulates Characterization](https://mlsanity.com/paper/2101.01676/) (2021)

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

- [Can we forget how we learned? Doxastic redundancy in iterated belief revision](https://mlsanity.com/paper/2402.15445/) (2024)
- [On Definite Iterated Belief Revision with Belief Algebras](https://mlsanity.com/paper/2505.06505/) (2025)

## Abstract (arXiv)

Iterated belief revision requires information about the current beliefs. This information is represented by mathematical structures called doxastic states. Most literature concentrates on how to revise a doxastic state and neglects that it may exponentially grow. This problem is studied for the most common ways of storing a doxastic state. All four methods are able to store every doxastic state, but some do it in less space than others. In particular, the explicit representation (an enumeration of the current beliefs) is the more wasteful on space. The level representation (a sequence of propositional formulae) and the natural representation (a history of natural revisions) are more compact than it. The lexicographic representation (a history of lexicographic revision) is even more compact than them.