Pushing the Boundaries of Natural Reasoning: Interleaved Bonus from Formal-Logic Verification

• URL: http://arxiv.org/abs/2601.22642v1
• Date: Fri, 30 Jan 2026 07:01:25 GMT
• Title: Pushing the Boundaries of Natural Reasoning: Interleaved Bonus from Formal-Logic Verification
• Authors: Chuxue Cao, Jinluan Yang, Haoran Li, Kunhao Pan, Zijian Zhao, Zhengyu Chen, Yuchen Tian, Lijun Wu, Conghui He, Sirui Han, Yike Guo,
• Abstract summary: Large Language Models (LLMs) show remarkable capabilities, yet their next-token prediction creates logical inconsistencies and reward hacking.<n>We introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process.<n>We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization.
• Score: 49.506412445511934
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4% and 14.2%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.

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