# MuSLR: Multimodal Symbolic Logical Reasoning

arXiv: https://arxiv.org/abs/2509.25851 · HTML: https://mlsanity.com/paper/2509.25851/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 38 of its 42 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 30 of 38)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [NExT-GPT: Any-to-Any Multimodal LLM](https://mlsanity.com/paper/2309.05519/) (2023)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [nocaps: novel object captioning at scale](https://mlsanity.com/paper/1812.08658/) (2018)
- [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)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [LogicVista: Multimodal LLM Logical Reasoning Benchmark in Visual Contexts](https://mlsanity.com/paper/2407.04973/) (2024)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Evaluation of Deep Convolutional Nets for Document Image Classification and Retrieval](https://mlsanity.com/paper/1502.07058/) (2015)
- [Multimodal Chain-of-Thought Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2503.12605/) (2025)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [VisuLogic: A Benchmark for Evaluating Visual Reasoning in Multi-modal Large Language Models](https://mlsanity.com/paper/2504.15279/) (2025)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models](https://mlsanity.com/paper/2404.15522/) (2024)
- [Vera: A General-Purpose Plausibility Estimation Model for Commonsense Statements](https://mlsanity.com/paper/2305.03695/) (2023)
- [Multi-LogiEval: Towards Evaluating Multi-Step Logical Reasoning Ability of Large Language Models](https://mlsanity.com/paper/2406.17169/) (2024)

## Built on by (most cited first, 7 of 7)

- [Similarity Is Not Logic: Factored Inference for Dual-Encoder Vision-Language Models](https://mlsanity.com/paper/2607.23052/) (2026)
- [Faithful Mobile GUI Agents with Guided Advantage Estimator](https://mlsanity.com/paper/2605.01208/) (2026)
- [VisualFLIP: Do Predictions Depend on Task-Critical Visual Evidence in Multimodal Reasoning?](https://mlsanity.com/paper/2606.07872/) (2026)
- [MaxSAT-Based Feedback for Guiding Vision-Language Models in Sudoku](https://mlsanity.com/paper/2607.12711/) (2026)
- [Decoupled Physical Modeling and Execution for Physics Reasoning](https://mlsanity.com/paper/2608.22126/) (2026)
- [Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning](https://mlsanity.com/paper/2603.12953/) (2026)
- [Hob-VL: A Benchmark for Visually Grounded Boolean Reasoning](https://mlsanity.com/paper/2610.01605/) (2026)

## Abstract (arXiv)

Multimodal symbolic logical reasoning, which aims to deduce new facts from multimodal input via formal logic, is critical in high-stakes applications such as autonomous driving and medical diagnosis, as its rigorous, deterministic reasoning helps prevent serious consequences. To evaluate such capabilities of current state-of-the-art vision language models (VLMs), we introduce the first benchmark MuSLR for multimodal symbolic logical reasoning grounded in formal logical rules. MuSLR comprises 1,093 instances across 7 domains, including 35 atomic symbolic logic and 976 logical combinations, with reasoning depths ranging from 2 to 9. We evaluate 7 state-of-the-art VLMs on MuSLR and find that they all struggle with multimodal symbolic reasoning, with the best model, GPT-4.1, achieving only 46.8%. Thus, we propose LogiCAM, a modular framework that applies formal logical rules to multimodal inputs, boosting GPT-4.1's Chain-of-Thought performance by 14.13%, and delivering even larger gains on complex logics such as first-order logic. We also conduct a comprehensive error analysis, showing that around 70% of failures stem from logical misalignment between modalities, offering key insights to guide future improvements. All data and code are publicly available at https://llm-symbol.github.io/MuSLR.