# A Kripke-Lewis semantics for belief update and belief revision

arXiv: https://arxiv.org/abs/2310.11506 · HTML: https://mlsanity.com/paper/2310.11506/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2023.

## Built on by (most cited first, 4 of 4)

- [A modal logic translation of the AGM axioms for belief revision](https://mlsanity.com/paper/2502.14176/) (2025)
- [On Definite Iterated Belief Revision with Belief Algebras](https://mlsanity.com/paper/2505.06505/) (2025)
- [The logic of KM belief update is contained in the logic of AGM belief revision](https://mlsanity.com/paper/2602.23302/) (2026)
- [Selective Credibility-Limited Belief Update](https://mlsanity.com/paper/2607.28523/) (2026)

## Abstract (arXiv)

We provide a new characterization of both belief update and belief revision in terms of a Kripke-Lewis semantics. We consider frames consisting of a set of states, a Kripke belief relation and a Lewis selection function. Adding a valuation to a frame yields a model. Given a model and a state, we identify the initial belief set K with the set of formulas that are believed at that state and we identify either the updated belief set or the revised belief set, prompted by the input represented by formula A, as the set of formulas that are the consequent of conditionals that (1) are believed at that state and (2) have A as antecedent. We show that this class of models characterizes both the Katsuno-Mendelzon (KM) belief update functions and the AGM belief revision functions, in the following sense: (1) each model gives rise to a partial belief function that can be completed into a full KM/AGM update/revision function, and (2) for every KM/AGM update/revision function there is a model whose associated belief function coincides with it. The difference between update and revision can be reduced to two semantic properties that appear in a stronger form in revision relative to update, thus confirming the finding by Peppas et al. (1996) that, "for a fixed theory K, revising K is much the same as updating K"