LogicReward: Incentivizing LLM Reasoning via Step-Wise Logical Supervision

Jundong Xu, Hao Fei, Huichi Zhou, Xin Quan, Qijun Huang, Shengqiong Wu, William Yang Wang, Mong-Li Lee, Wynne Hsu

Track: long paper (up to 10 pages)

Keywords: reasoning, logic, reinforcement learning, neuro-symbolic

TL;DR: We introduce LogicReward, a reward function that evaluates unstructured natural language reasoning and provides step-level, symbolically guided rewards, which guides LLMs to reason better.

Abstract: Although LLMs exhibit strong reasoning capabilities, existing training methods largely depend on outcome-based feedback, which can produce correct answers with flawed reasoning. Prior work introduces supervision on intermediate steps but still lacks guarantees of logical soundness, which is crucial in high-stakes scenarios where logical consistency is paramount. To address this, we propose LogicReward, a novel reward system that guides model training by enforcing step-level logical correctness with a theorem prover. We further introduce Autoformalization with Soft Unification, which reduces natural language ambiguity and improves formalization quality, enabling more effective use of the theorem prover. An 8B model trained on data constructed with LogicReward surpasses GPT-4o and o4-mini by 11.6% and 2% on natural language inference and logical reasoning tasks with simple training procedures. Further analysis shows that LogicReward enhances reasoning faithfulness, improves generalizability to unseen tasks such as math and commonsense reasoning, and provides a reliable reward signal even without ground-truth labels.

Presenter: ~Jundong_Xu1

Format: Yes, the presenting author will definitely attend in person because they attending ICLR for other complementary reasons.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Funding: No, the presenting author of this submission does *not* fall under ICLR’s funding aims, or has sufficient alternate funding.

Submission Number: 39