# NL2LOGIC: AST-Guided Translation of Natural Language into First-Order Logic with Large Language Models

arXiv: https://arxiv.org/abs/2602.13237 · HTML: https://mlsanity.com/paper/2602.13237/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 45 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 21 of 21)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [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)
- [Constituency Parsing with a Self-Attentive Encoder](https://mlsanity.com/paper/1805.01052/) (2018)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Multilingual Constituency Parsing with Self-Attention and Pre-Training](https://mlsanity.com/paper/1812.11760/) (2018)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Reasoning about Entailment with Neural Attention](https://mlsanity.com/paper/1509.06664/) (2015)
- [Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation](https://mlsanity.com/paper/2305.15541/) (2023)
- [Segment Any Text: A Universal Approach for Robust, Efficient and Adaptable Sentence Segmentation](https://mlsanity.com/paper/2406.16678/) (2024)
- [Verification and Refinement of Natural Language Explanations through LLM-Symbolic Theorem Proving](https://mlsanity.com/paper/2405.01379/) (2024)
- [FaiRR: Faithful and Robust Deductive Reasoning over Natural Language](https://mlsanity.com/paper/2203.10261/) (2022)
- [Enhancing Reasoning Capabilities of LLMs via Principled Synthetic Logic Corpus](https://mlsanity.com/paper/2411.12498/) (2024)
- [Semantic Parsing with Dual Learning](https://mlsanity.com/paper/1907.05343/) (2019)
- [Can Neural Networks Understand Logical Entailment?](https://mlsanity.com/paper/1802.08535/) (2018)
- [Where's the Point? Self-Supervised Multilingual Punctuation-Agnostic Sentence Segmentation](https://mlsanity.com/paper/2305.18893/) (2023)
- [LangPro: Natural Language Theorem Prover](https://mlsanity.com/paper/1708.09417/) (2017)
- [Faithful and Robust LLM-Driven Theorem Proving for NLI Explanations](https://mlsanity.com/paper/2505.24264/) (2025)

## Built on by (most cited first, 5 of 5)

- [CTIFoundry: An Agent-Native Corpus Scaffold for Cyber Threat Intelligence](https://mlsanity.com/paper/2608.18613/) (2026)
- [Reasoners or Translators? Contamination-aware Evaluation and Neuro-Symbolic Robustness in Tax Law](https://mlsanity.com/paper/2605.16052/) (2026)
- [Instruct, Not Answer: Using Instruction Privileges in On-Policy Context Distillation](https://mlsanity.com/paper/2609.32201/) (2026)
- [SpecForge: Recursive Self-Improvement for Coding Agents via Behavioral Specifications](https://mlsanity.com/paper/2610.15708/) (2026)
- [Small but Mighty: Test Suites as Improvement Signals for Self-Evolving Agents](https://mlsanity.com/paper/2610.15964/) (2026)

## Abstract (arXiv)

Automated reasoning is critical in domains such as law and governance, where verifying claims against facts in documents requires both accuracy and interpretability. Recent work adopts structured reasoning pipelines that translate natural language into first-order logic and delegate inference to automated solvers. With the rise of large language models, approaches such as GCD and CODE4LOGIC leverage their reasoning and code generation capabilities to improve logic parsing. However, these methods suffer from fragile syntax control due to weak enforcement of global grammar constraints and low semantic faithfulness caused by insufficient clause-level semantic understanding. We propose NL2LOGIC, a first-order logic translation framework that introduces an abstract syntax tree as an intermediate representation. NL2LOGIC combines a recursive large language model based semantic parser with an abstract syntax tree guided generator that deterministically produces solver-ready logic code. Experiments on the FOLIO, LogicNLI, and ProofWriter benchmarks show that NL2LOGIC achieves 99 percent syntactic accuracy and improves semantic correctness by up to 30 percent over state-of-the-art baselines. Furthermore, integrating NL2LOGIC into Logic-LM yields near-perfect executability and improves downstream reasoning accuracy by 31 percent compared to Logic-LM's original few-shot unconstrained translation module.