# LogicReward: Incentivizing LLM Reasoning via Step-Wise Logical Supervision

arXiv: https://arxiv.org/abs/2512.18196 · HTML: https://mlsanity.com/paper/2512.18196/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 60 of its 68 references that are in the map.
- First posted on arXiv 20 Dec 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 60)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [e-SNLI: Natural Language Inference with Natural Language Explanations](https://mlsanity.com/paper/1812.01193/) (2018)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [QASC: A Dataset for Question Answering via Sentence Composition](https://mlsanity.com/paper/1910.11473/) (2019)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)

## Built on by (most cited first, 6 of 6)

- [Correct Prediction, Wrong Steps? Consensus Reasoning Knowledge Graph for Robust Chain-of-Thought Synthesis](https://mlsanity.com/paper/2604.14121/) (2026)
- [Uncovering the Representation Geometry of Minimal Cores in Overcomplete Reasoning Traces](https://mlsanity.com/paper/2605.14358/) (2026)
- [Decompose-and-Formalise: Recursively Verifiable Natural Language Inference](https://mlsanity.com/paper/2601.19605/) (2026)
- [GeoFaith: A Spatio-Temporal Dual View of Faithful Chain-of-Thought](https://mlsanity.com/paper/2605.26893/) (2026)
- [SymDiag: Explainable Diagnosis for LLM Reasoning via Neuro-Symbolic Verification](https://mlsanity.com/paper/2608.08786/) (2026)
- [Learning to Prove, Not Just to Answer: Reinforcement Learning from Formal Verification for Natural-Language Logical Reasoning](https://mlsanity.com/paper/2609.37203/) (2026)

## Abstract (arXiv)

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.