[2603.29500] Learning to Generate Formally Verifiable Step-by-Step Logic Reasoning via Structured Formal Intermediaries

Computer Science > Artificial Intelligence arXiv:2603.29500 (cs) [Submitted on 31 Mar 2026] Title:Learning to Generate Formally Verifiable Step-by-Step Logic Reasoning via Structured Formal Intermediaries Authors:Luoxin Chen, Yichi Zhou, Huishuai Zhang View a PDF of the paper titled Learning to Generate Formally Verifiable Step-by-Step Logic Reasoning via Structured Formal Intermediaries, by Luoxin Chen and 2 other authors View PDF HTML (experimental) Abstract:Large language models (LLMs) have recently demonstrated impressive performance on complex, multi-step reasoning tasks, especially when post-trained with outcome-rewarded reinforcement learning Guo et al. 2025. However, it has been observed that outcome rewards often overlook flawed intermediate steps, leading to unreliable reasoning steps even when final answers are correct. To address this unreliable reasoning, we propose PRoSFI (Process Reward over Structured Formal Intermediates), a novel reward method that enhances reasoning reliability without compromising accuracy. Instead of generating formal proofs directly, which is rarely accomplishable for a modest-sized (7B) model, the model outputs structured intermediate steps aligned with its natural language reasoning. Each step is then verified by a formal prover. Only fully validated reasoning chains receive high rewards. The integration of formal verification guides the model towards generating step-by-step machine-checkable proofs, thereby yielding more credible f...