@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://aclanthology.org/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."
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%0 Conference Proceedings
%T FLAIR: Steering LLM Mathematical Problem Solving based on A Fuzzy-Logic-AssIsted Reasoner
%A Wu, Hao
%A Sun, Hongru
%A Li, Wanqing
%A Yu, Xinguo
%A Ming, Hao
%A Luo, Xiao
%A Zhang, Wenbin
%A Zhao, Jiahong
%A Guo, Yi
%A Yang, Jie
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F wu-etal-2026-flair
%X 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.
%U https://aclanthology.org/2026.acl-long.1790/
%P 38638-38661
Markdown (Informal)
[FLAIR: Steering LLM Mathematical Problem Solving based on A Fuzzy-Logic-AssIsted Reasoner](https://aclanthology.org/2026.acl-long.1790/) (Wu et al., ACL 2026)
ACL
- Hao Wu, Hongru Sun, Wanqing Li, Xinguo Yu, Hao Ming, Xiao Luo, Wenbin Zhang, Jiahong Zhao, Yi Guo, and Jie Yang. 2026. FLAIR: Steering LLM Mathematical Problem Solving based on A Fuzzy-Logic-AssIsted Reasoner. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 38638–38661, San Diego, California, United States. Association for Computational Linguistics.