# Inductive Learning of Logical Theories with LLMs: An Expressivity-Graded Analysis

arXiv: https://arxiv.org/abs/2408.16779 · HTML: https://mlsanity.com/paper/2408.16779/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2024.

## Built on by (most cited first, 6 of 6)

- [Logical Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2502.09100/) (2025)
- [Faithful and Robust LLM-Driven Theorem Proving for NLI Explanations](https://mlsanity.com/paper/2505.24264/) (2025)
- [PEIRCE: Unifying Material and Formal Reasoning via LLM-Driven Neuro-Symbolic Refinement](https://mlsanity.com/paper/2504.04110/) (2025)
- [Visual Perceptual to Conceptual First-Order Rule Learning Networks](https://mlsanity.com/paper/2604.07897/) (2026)
- [ADVENT: LLM-Driven Automatic Predicate Invention for ILP](https://mlsanity.com/paper/2607.01585/) (2026)
- [Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming](https://mlsanity.com/paper/2607.23019/) (2026)

## Abstract (arXiv)

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t. rule dependency structure, allowing quantification of specific inference challenges on LLM performance. Integrating LLMs with formal methods is a promising frontier in the Natural Language Processing field, as an important avenue for improving model inference control and explainability. In particular, inductive learning over complex sets of facts and rules, poses unique challenges for current autoregressive models, as they lack explicit symbolic grounding. While they can be complemented by formal systems, the properties delivered by LLMs regarding inductive learning, are not well understood and quantified. Empirical results indicate that the largest LLMs can achieve competitive results against a SOTA Inductive Logic Programming (ILP) system baseline, but also that tracking long predicate relationship chains is a more difficult obstacle than theory complexity for LLMs.