# Learning big logical rules by joining small rules

arXiv: https://arxiv.org/abs/2401.16215 · HTML: https://mlsanity.com/paper/2401.16215/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 14 of 14)

- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [RobustFill: Neural Program Learning under Noisy I/O](https://mlsanity.com/paper/1703.07469/) (2017)
- [Leveraging Grammar and Reinforcement Learning for Neural Program Synthesis](https://mlsanity.com/paper/1805.04276/) (2018)
- [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)
- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [Making sense of sensory input](https://mlsanity.com/paper/1910.02227/) (2019)
- [Synthesizing Datalog Programs Using Numerical Relaxation](https://mlsanity.com/paper/1906.00163/) (2019)
- [Inductive general game playing](https://mlsanity.com/paper/1906.09627/) (2019)
- [CrossBeam: Learning to Search in Bottom-Up Program Synthesis](https://mlsanity.com/paper/2203.10452/) (2022)
- [Learning MDL logic programs from noisy data](https://mlsanity.com/paper/2308.09393/) (2023)
- [Learning Relational Representations with Auto-encoding Logic Programs](https://mlsanity.com/paper/1903.12577/) (2019)
- [Learning logic programs by combining programs](https://mlsanity.com/paper/2206.01614/) (2022)
- [Towards meta-interpretive learning of programming language semantics](https://mlsanity.com/paper/1907.08834/) (2019)

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

- [From Code to Play: Benchmarking Program Search for Games Using Large Language Models](https://mlsanity.com/paper/2412.04057/) (2024)
- [Shedding Light in Task Decomposition in Program Synthesis: The Driving Force of the Synthesizer Model](https://mlsanity.com/paper/2503.08738/) (2025)
- [Honey, I shrunk the hypothesis space (through logical preprocessing)](https://mlsanity.com/paper/2506.06739/) (2025)
- [Visual Perceptual to Conceptual First-Order Rule Learning Networks](https://mlsanity.com/paper/2604.07897/) (2026)

## Abstract (arXiv)

A major challenge in inductive logic programming is learning big rules. To address this challenge, we introduce an approach where we join small rules to learn big rules. We implement our approach in a constraint-driven system and use constraint solvers to efficiently join rules. Our experiments on many domains, including game playing and drug design, show that our approach can (i) learn rules with more than 100 literals, and (ii) drastically outperform existing approaches in terms of predictive accuracies.