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.
@article{arxiv.2509.25851,
title = {MuSLR: Multimodal Symbolic Logical Reasoning},
author = {Jundong Xu and Hao Fei and Yuhui Zhang and Liangming Pan and Qijun Huang and Qian Liu and Preslav Nakov and Min-Yen Kan and William Yang Wang and Mong-Li Lee and Wynne Hsu},
journal= {arXiv preprint arXiv:2509.25851},
year = {2026}
}