# Abductive Logical Rule Induction by Bridging Inductive Logic Programming and Multimodal Large Language Models

arXiv: https://arxiv.org/abs/2509.21874 · HTML: https://mlsanity.com/paper/2509.21874/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 45 of its 56 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 45)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Multi-Concept Customization of Text-to-Image Diffusion](https://mlsanity.com/paper/2212.04488/) (2022)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [CogVLM: Visual Expert for Pretrained Language Models](https://mlsanity.com/paper/2311.03079/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [Mix-of-Show: Decentralized Low-Rank Adaptation for Multi-Concept Customization of Diffusion Models](https://mlsanity.com/paper/2305.18292/) (2023)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [Language models show human-like content effects on reasoning tasks](https://mlsanity.com/paper/2207.07051/) (2022)
- [Compositional Chain-of-Thought Prompting for Large Multimodal Models](https://mlsanity.com/paper/2311.17076/) (2023)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [Deductive Verification of Chain-of-Thought Reasoning](https://mlsanity.com/paper/2306.03872/) (2023)
- [Chain of Code: Reasoning with a Language Model-Augmented Code Emulator](https://mlsanity.com/paper/2312.04474/) (2023)
- [Hypothesis Search: Inductive Reasoning with Language Models](https://mlsanity.com/paper/2309.05660/) (2023)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)

## Built on by (most cited first, 3 of 3)

- [A Foundation Model for Zero-Shot Logical Rule Induction](https://mlsanity.com/paper/2605.04916/) (2026)
- [ADVENT: LLM-Driven Automatic Predicate Invention for ILP](https://mlsanity.com/paper/2607.01585/) (2026)
- [When the Canonical Completion Is Wrong: Formalizing and Measuring the Jump in Large Language Models](https://mlsanity.com/paper/2608.26187/) (2026)

## Abstract (arXiv)

We propose ILP-CoT, a method that bridges Inductive Logic Programming (ILP) and Multimodal Large Language Models (MLLMs) for abductive logical rule induction. The task involves both discovering logical facts and inducing logical rules from a small number of unstructured textual or visual inputs, which still remain challenging when solely relying on ILP, due to the requirement of specified background knowledge and high computational cost, or MLLMs, due to the appearance of perceptual hallucinations. Based on the key observation that MLLMs could propose structure-correct rules even under hallucinations, our approach automatically builds ILP tasks with pruned search spaces based on the rule structure proposals from MLLMs, and utilizes ILP system to output rules built upon rectified logical facts and formal inductive reasoning. Its effectiveness is verified through challenging logical induction benchmarks, as well as a potential application of our approach, namely text-to-image customized generation with rule induction. Our code and data are released at https://github.com/future-item/ILP-CoT.