# Effective AGM Belief Contraction: A Journey beyond the Finitary Realm (Technical Report)

arXiv: https://arxiv.org/abs/2409.09171 · HTML: https://mlsanity.com/paper/2409.09171/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 55 references that are in the map.
- First posted on arXiv 13 Sep 2024.

## Builds on (most cited first, 1 of 1)

- [On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic](https://mlsanity.com/paper/1401.3902/) (2014)

## Abstract (arXiv)

Despite significant efforts towards extending the AGM paradigm of belief change beyond finitary logics, the computational aspects of AGM have remained almost untouched. We investigate the computability of AGM contraction on non-finitary logics, and show an intriguing negative result: there are infinitely many uncomputable AGM contraction functions in such logics. Drastically, we also show that the current de facto standard strategies to control computability, which rely on restricting the space of epistemic states, fail: uncomputability remains in all non-finitary cases. Motivated by this disruptive result, we propose new approaches to controlling computability beyond the finitary realm. Using Linear Temporal Logic (LTL) as a case study, we identify an infinite class of fully-rational AGM contraction functions that are computable by design. We use B"uchi automata to construct such functions, and to represent and reason about LTL beliefs.