@inproceedings{wu-etal-2026-flair,
    title = "{FLAIR}: Steering {LLM} Mathematical Problem Solving based on A Fuzzy-Logic-{A}ss{I}sted Reasoner",
    author = "Wu, Hao  and
      Sun, Hongru  and
      Li, Wanqing  and
      Yu, Xinguo  and
      Ming, Hao  and
      Luo, Xiao  and
      Zhang, Wenbin  and
      Zhao, Jiahong  and
      Guo, Yi  and
      Yang, Jie",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Proceedings of the 64th Annual Meeting of the {A}ssociation for {C}omputational {L}inguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.acl-long.1790/",
    pages = "38638--38661",
    ISBN = "979-8-89176-390-6",
    abstract = "Mathematical reasoning is one of the core capabilities for Large Language Models (LLMs). Yet, existing approaches often rely on static heuristics or pre-determined reasoning strategies, limiting their ability to adapt to different intermediate states. To address this limitation, we propose FLAIR (Fuzzy-Logic-AssIsted Reasoner), an adaptive framework that integrates fuzzy theory into LLM-based mathematical reasoning. Specifically, FLAIR characterizes intermediate problem-solving states using fuzzy memberships and employs a parameterized fuzzy rule system to conditionally activate subsequent actions. These rule parameters are further adjusted via Reinforcement Learning using solution-level feedback as the reward signal, enabling adaptive and iterative refinement without reliance on a fixed strategy. To the best of our knowledge, this work is the first to integrate fuzzy theory into LLM-based mathematical reasoning. Extensive experiments across multiple benchmarks demonstrate that FLAIR consistently outperforms recent state-of-the-art baselines, while offering effective and interpretable diagnostics of intermediate problem-solving states."
}