# Learning Logical Rules using Minimum Message Length

arXiv: https://arxiv.org/abs/2508.06230 · HTML: https://mlsanity.com/paper/2508.06230/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 52 references that are in the map.
- First posted on arXiv 8 Aug 2025.

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

- [Inductive logic programming at 30: a new introduction](https://mlsanity.com/paper/2008.07912/) (2020)
- [LLMs and the Abstraction and Reasoning Corpus: Successes, Failures, and the Importance of Object-based Representations](https://mlsanity.com/paper/2305.18354/) (2023)
- [Learning programs by learning from failures](https://mlsanity.com/paper/2005.02259/) (2020)
- [Learning MDL logic programs from noisy data](https://mlsanity.com/paper/2308.09393/) (2023)
- [Learning logic programs by discovering where not to search](https://mlsanity.com/paper/2202.09806/) (2022)
- [Introduction to minimum message length inference](https://mlsanity.com/paper/2209.14571/) (2022)

## Built on by (most cited first, 1 of 1)

- [Compressing Chemistry Reveals Functional Groups](https://mlsanity.com/paper/2511.05728/) (2025)

## Abstract (arXiv)

Unifying probabilistic and logical learning is a key challenge in AI. We introduce a Bayesian inductive logic programming approach that learns minimum message length hypotheses from noisy data. Our approach balances hypothesis complexity and data fit through priors, which favour more general programs, and a likelihood, which favours accurate programs. Our experiments on several domains, including game playing and drug design, show that our method significantly outperforms previous methods, notably those that learn minimum description length programs. Our results also show that our approach is data-efficient and insensitive to example balance, including the ability to learn from exclusively positive examples.