FLAIR: Steering LLM Mathematical Problem Solving based on A Fuzzy-Logic-AssIsted Reasoner
Hao Wu, Hongru Sun University of Wollongong, Wanqing Li University of Wollongong, Xinguo Yu, Hao Ming, Xiao Luo University of Wisconsin - Madison, Wenbin Zhang Florida International University, Jiahong Zhao University of Southampton 等 10 位作者
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.
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Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表