# LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers

arXiv: https://arxiv.org/abs/2310.15164 · HTML: https://mlsanity.com/paper/2310.15164/

## Key facts

- Cited by 168 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 46 of its 92 references that are in the map.
- First posted on arXiv 23 Oct 2023.

## Placed in

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

## Builds on (most cited first, 30 of 46)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [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)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Augmented Language Models: a Survey](https://mlsanity.com/paper/2302.07842/) (2023)
- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [The Stack: 3 TB of permissively licensed source code](https://mlsanity.com/paper/2211.15533/) (2022)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Autoformalization with Large Language Models](https://mlsanity.com/paper/2205.12615/) (2022)
- [Efficient Training of Language Models to Fill in the Middle](https://mlsanity.com/paper/2207.14255/) (2022)
- [Binding Language Models in Symbolic Languages](https://mlsanity.com/paper/2210.02875/) (2022)
- [Is Self-Repair a Silver Bullet for Code Generation?](https://mlsanity.com/paper/2306.09896/) (2023)
- [ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics](https://mlsanity.com/paper/2302.12433/) (2023)
- [From Word Models to World Models: Translating from Natural Language to the Probabilistic Language of Thought](https://mlsanity.com/paper/2306.12672/) (2023)
- [Self-Edit: Fault-Aware Code Editor for Code Generation](https://mlsanity.com/paper/2305.04087/) (2023)

## Built on by (most cited first, 30 of 168)

- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [SynCode: LLM Generation with Grammar Augmentation](https://mlsanity.com/paper/2403.01632/) (2024)
- [A Survey on LLM-based Code Generation for Low-Resource and Domain-Specific Programming Languages](https://mlsanity.com/paper/2410.03981/) (2024)
- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)
- [Puzzle Solving using Reasoning of Large Language Models: A Survey](https://mlsanity.com/paper/2402.11291/) (2024)
- [Neuro-Symbolic AI in 2024: A Systematic Review](https://mlsanity.com/paper/2501.05435/) (2025)
- [How Far Can Transformers Reason? The Globality Barrier and Inductive Scratchpad](https://mlsanity.com/paper/2406.06467/) (2024)
- [Verification and Refinement of Natural Language Explanations through LLM-Symbolic Theorem Proving](https://mlsanity.com/paper/2405.01379/) (2024)
- [Can LLMs Reason with Rules? Logic Scaffolding for Stress-Testing and Improving LLMs](https://mlsanity.com/paper/2402.11442/) (2024)
- [Divide and Translate: Compositional First-Order Logic Translation and Verification for Complex Logical Reasoning](https://mlsanity.com/paper/2410.08047/) (2024)
- [LogicAD: Explainable Anomaly Detection via VLM-based Text Feature Extraction](https://mlsanity.com/paper/2501.01767/) (2025)
- [Theory of Mind in Large Language Models: Assessment and Enhancement](https://mlsanity.com/paper/2505.00026/) (2025)
- [Mathematical Language Models: A Survey](https://mlsanity.com/paper/2312.07622/) (2023)
- [Logic-of-Thought: Injecting Logic into Contexts for Full Reasoning in Large Language Models](https://mlsanity.com/paper/2409.17539/) (2024)
- [Fast Controlled Generation from Language Models with Adaptive Weighted Rejection Sampling](https://mlsanity.com/paper/2504.05410/) (2025)
- [Learning to Reason via Mixture-of-Thought for Logical Reasoning](https://mlsanity.com/paper/2505.15817/) (2025)
- [Symbolic Working Memory Enhances Language Models for Complex Rule Application](https://mlsanity.com/paper/2408.13654/) (2024)
- [Constrained Discrete Diffusion](https://mlsanity.com/paper/2503.09790/) (2025)
- [Dissecting Logical Reasoning in LLMs: A Fine-Grained Evaluation and Supervision Study](https://mlsanity.com/paper/2506.04810/) (2025)
- [Enhancing Ethical Explanations of Large Language Models through Iterative Symbolic Refinement](https://mlsanity.com/paper/2402.00745/) (2024)
- [CoMAT: Chain of Mathematically Annotated Thought Improves Mathematical Reasoning](https://mlsanity.com/paper/2410.10336/) (2024)
- [Search, Verify and Feedback: Towards Next Generation Post-training Paradigm of Foundation Models via Verifier Engineering](https://mlsanity.com/paper/2411.11504/) (2024)
- [RL for Reasoning by Adaptively Revealing Rationales](https://mlsanity.com/paper/2506.18110/) (2025)
- [NeSyC: A Neuro-symbolic Continual Learner For Complex Embodied Tasks In Open Domains](https://mlsanity.com/paper/2503.00870/) (2025)
- [Reliable Reasoning Beyond Natural Language](https://mlsanity.com/paper/2407.11373/) (2024)
- [Theorem Prover as a Judge for Synthetic Data Generation](https://mlsanity.com/paper/2502.13137/) (2025)

## Abstract (arXiv)

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/linc