Training LLMs with LogicReward for Faithful and Rigorous Reasoning

• URL: http://arxiv.org/abs/2512.18196v1
• Date: Sat, 20 Dec 2025 03:43:02 GMT
• Title: Training LLMs with LogicReward for Faithful and Rigorous Reasoning
• Authors: Jundong Xu, Hao Fei, Huichi Zhou, Xin Quan, Qijun Huang, Shengqiong Wu, William Yang Wang, Mong-Li Lee, Wynne Hsu,
• Abstract summary: We propose LogicReward, a reward system that guides model training by enforcing step-level logical correctness with a theorem prover.<n>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.
• Score: 75.30425553246177
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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. We will release all data and code at https://llm-symbol.github.io/LogicReward.

Related papers

• Beyond Correctness: Learning Robust Reasoning via Transfer [51.403609251508904]
  We adopt a simple philosophical view, robust reasoning should remain useful beyond the mind that produced it.<n>We introduce Reinforcement Learning with Transferable Reward, which operationalizes robustness via transfer reward.<n>Our approach improves sampling consistency while improving final answer accuracy, and it reaches comparable performance in substantially fewer training steps.
  arXiv  Detail & Related papers  (2026-02-09T10:41:44Z)
• A Balanced Neuro-Symbolic Approach for Commonsense Abductive Logic [21.003276503456632]
  We propose a novel method to augment a logic problem with commonsense relations provided by the Large Language Models.<n>This involves a search procedure through potential commonsense assumptions to maximize the chance of finding useful facts.
  arXiv  Detail & Related papers  (2026-01-26T15:40:26Z)
• Making Mathematical Reasoning Adaptive [61.45161826629692]
  We propose the AdaR framework to enable adaptive reasoning in large language models (LLMs)<n>AdaR synthesizes logically equivalent queries by varying variable values, and trains models with RLVR on these data to penalize spurious logic.<n> Experimental results demonstrate that AdaR improves robustness and generalization, achieving substantial improvement in mathematical reasoning.
  arXiv  Detail & Related papers  (2025-10-06T09:30:05Z)
• Rethinking Reasoning Quality in Large Language Models through Enhanced Chain-of-Thought via RL [19.659532349434418]
  Reinforcement learning (RL) has recently become the dominant paradigm for strengthening the reasoning abilities of large language models.<n>Yet the rule-based reward functions commonly used on mathematical or programming benchmarks assess only answer format and correctness.<n>We propose Dynamic Reasoning Efficiency Reward (DRER) -- a plug-and-play RL reward framework that reshapes both reward and advantage signals.
  arXiv  Detail & Related papers  (2025-09-07T11:52:18Z)
• Learning to Reason via Mixture-of-Thought for Logical Reasoning [56.24256916896427]
  Mixture-of-Thought (MoT) is a framework that enables LLMs to reason across three complementary modalities: natural language, code, and truth-table.<n>MoT adopts a two-phase design: (1) self-evolving MoT training, which jointly learns from filtered, self-generated rationales across modalities; and (2) MoT inference, which fully leverages the synergy of three modalities to produce better predictions.
  arXiv  Detail & Related papers  (2025-05-21T17:59:54Z)
• Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning [23.99454995087634]
  We explore the potential of rule-based reinforcement learning in large reasoning models.<n>We use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification.<n>Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus.
  arXiv  Detail & Related papers  (2025-02-20T17:49:26Z)
• LogicAsker: Evaluating and Improving the Logical Reasoning Ability of Large Language Models [63.14196038655506]
  We introduce LogicAsker, a novel approach for evaluating and enhancing the logical reasoning capabilities of large language models (LLMs) Our methodology reveals significant gaps in LLMs' learning of logical rules, with identified reasoning failures ranging from 29% to 90% across different models. We leverage these findings to construct targeted demonstration examples and fine-tune data, notably enhancing logical reasoning in models like GPT-4o by up to 5%.
  arXiv  Detail & Related papers  (2024-01-01T13:53:53Z)
• LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers [60.009969929857704]
  Logical reasoning is an important task for artificial intelligence with potential impacts on science, mathematics, and society. In this work, we reformulating such tasks as modular neurosymbolic programming, which we call LINC. We observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate.
  arXiv  Detail & Related papers  (2023-10-23T17:58:40Z)
• QA-NatVer: Question Answering for Natural Logic-based Fact Verification [11.002475880349452]
  We propose to use question answering to predict natural logic operators. In a few-shot setting on FEVER, our approach outperforms the best baseline by $4.3$ accuracy points. A human evaluation indicates that our approach produces more plausible with fewer erroneous natural logic operators than previous natural logic-based systems.
  arXiv  Detail & Related papers  (2023-10-22T06:27:31Z)
• Towards LogiGLUE: A Brief Survey and A Benchmark for Analyzing Logical Reasoning Capabilities of Language Models [56.34029644009297]
  Large language models (LLMs) have demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. LLMs excel most in abductive reasoning, followed by deductive reasoning, while they are least effective at inductive reasoning. We study single-task training, multi-task training, and "chain-of-thought" knowledge distillation fine-tuning technique to assess the performance of model.
  arXiv  Detail & Related papers  (2023-10-02T01:00:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.