# Logical Rule Induction and Theory Learning Using Neural Theorem Proving

arXiv: https://arxiv.org/abs/1809.02193 · HTML: https://mlsanity.com/paper/1809.02193/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2018.

## Built on by (most cited first, 13 of 13)

- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Neuro-Symbolic Hierarchical Rule Induction](https://mlsanity.com/paper/2112.13418/) (2021)
- [Neural Compositional Rule Learning for Knowledge Graph Reasoning](https://mlsanity.com/paper/2303.03581/) (2023)
- [On the Correspondence Between Monotonic Max-Sum GNNs and Datalog](https://mlsanity.com/paper/2305.18015/) (2023)
- [Latent Logic Tree Extraction for Event Sequence Explanation from LLMs](https://mlsanity.com/paper/2406.01124/) (2024)
- [Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learning](https://mlsanity.com/paper/2305.12738/) (2023)
- [Neuro-symbolic Rule Learning in Real-world Classification Tasks](https://mlsanity.com/paper/2303.16674/) (2023)
- [Neuro-Symbolic Temporal Point Processes](https://mlsanity.com/paper/2406.03914/) (2024)
- [Temporal Inductive Logic Reasoning over Hypergraphs](https://mlsanity.com/paper/2206.05051/) (2022)
- [Knowledge Enhanced Neural Networks for relational domains](https://mlsanity.com/paper/2205.15762/) (2022)
- [Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rules](https://mlsanity.com/paper/2409.16238/) (2024)
- [Logic of Hypotheses: from Zero to Full Knowledge in Neurosymbolic Integration](https://mlsanity.com/paper/2509.21663/) (2025)
- [Neuro-Logic Lifelong Learning](https://mlsanity.com/paper/2511.12793/) (2025)

## Abstract (arXiv)

A hallmark of human cognition is the ability to continually acquire and distill observations of the world into meaningful, predictive theories. In this paper we present a new mechanism for logical theory acquisition which takes a set of observed facts and learns to extract from them a set of logical rules and a small set of core facts which together entail the observations. Our approach is neuro-symbolic in the sense that the rule pred- icates and core facts are given dense vector representations. The rules are applied to the core facts using a soft unification procedure to infer additional facts. After k steps of forward inference, the consequences are compared to the initial observations and the rules and core facts are then encouraged towards representations that more faithfully generate the observations through inference. Our approach is based on a novel neural forward-chaining differentiable rule induction network. The rules are interpretable and learned compositionally from their predicates, which may be invented. We demonstrate the efficacy of our approach on a variety of ILP rule induction and domain theory learning datasets.