# Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning

arXiv: https://arxiv.org/abs/2305.12295 · HTML: https://mlsanity.com/paper/2305.12295/

## Key facts

- Cited by 391 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 41 of its 67 references that are in the map.
- First posted on arXiv 20 May 2023.

## Placed in

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

## Builds on (most cited first, 30 of 41)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Energy and Policy Considerations for Deep Learning in NLP](https://mlsanity.com/paper/1906.02243/) (2019)
- [HuggingGPT: Solving AI Tasks with ChatGPT and its Friends in Hugging Face](https://mlsanity.com/paper/2303.17580/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [REPLUG: Retrieval-Augmented Black-Box Language Models](https://mlsanity.com/paper/2301.12652/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [LLM+P: Empowering Large Language Models with Optimal Planning Proficiency](https://mlsanity.com/paper/2304.11477/) (2023)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [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)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Evaluating the Logical Reasoning Ability of ChatGPT and GPT-4](https://mlsanity.com/paper/2304.03439/) (2023)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)

## Built on by (most cited first, 30 of 391)

- [OpenHands: An Open Platform for AI Software Developers as Generalist Agents](https://mlsanity.com/paper/2407.16741/) (2024)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [Automatically Correcting Large Language Models: Surveying the landscape of diverse self-correction strategies](https://mlsanity.com/paper/2308.03188/) (2023)
- [Leveraging Pre-trained Large Language Models to Construct and Utilize World Models for Model-based Task Planning](https://mlsanity.com/paper/2305.14909/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [LLMs Can't Plan, But Can Help Planning in LLM-Modulo Frameworks](https://mlsanity.com/paper/2402.01817/) (2024)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [SWE-Search: Enhancing Software Agents with Monte Carlo Tree Search and Iterative Refinement](https://mlsanity.com/paper/2410.20285/) (2024)
- [A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond](https://mlsanity.com/paper/2503.21614/) (2025)
- [From Word Models to World Models: Translating from Natural Language to the Probabilistic Language of Thought](https://mlsanity.com/paper/2306.12672/) (2023)
- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Large Language Models Can Learn Temporal Reasoning](https://mlsanity.com/paper/2401.06853/) (2024)
- [GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning](https://mlsanity.com/paper/2312.12241/) (2023)
- [Learning From Mistakes Makes LLM Better Reasoner](https://mlsanity.com/paper/2310.20689/) (2023)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Self-playing Adversarial Language Game Enhances LLM Reasoning](https://mlsanity.com/paper/2404.10642/) (2024)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [TableGPT2: A Large Multimodal Model with Tabular Data Integration](https://mlsanity.com/paper/2411.02059/) (2024)
- [SciAgent: Tool-augmented Language Models for Scientific Reasoning](https://mlsanity.com/paper/2402.11451/) (2024)
- [SynCode: LLM Generation with Grammar Augmentation](https://mlsanity.com/paper/2403.01632/) (2024)
- [Are Large Language Models Really Good Logical Reasoners? A Comprehensive Evaluation and Beyond](https://mlsanity.com/paper/2306.09841/) (2023)
- [Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation](https://mlsanity.com/paper/2305.15541/) (2023)
- [Can Language Models Learn to Skip Steps?](https://mlsanity.com/paper/2411.01855/) (2024)
- [Grammar Prompting for Domain-Specific Language Generation with Large Language Models](https://mlsanity.com/paper/2305.19234/) (2023)
- [Guiding Language Model Reasoning with Planning Tokens](https://mlsanity.com/paper/2310.05707/) (2023)
- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)

## Abstract (arXiv)

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical problem-solving. Our method first utilizes LLMs to translate a natural language problem into a symbolic formulation. Afterward, a deterministic symbolic solver performs inference on the formulated problem. We also introduce a self-refinement module, which utilizes the symbolic solver's error messages to revise symbolic formalizations. We demonstrate Logic-LM's effectiveness on five logical reasoning datasets: ProofWriter, PrOntoQA, FOLIO, LogicalDeduction, and AR-LSAT. On average, Logic-LM achieves a significant performance boost of 39.2% over using LLM alone with standard prompting and 18.4% over LLM with chain-of-thought prompting. Our findings suggest that Logic-LM, by combining LLMs with symbolic logic, offers a promising avenue for faithful logical reasoning. Code and data are publicly available at https://github.com/teacherpeterpan/Logic-LLM.