mlsanityData to 14 Oct 2026

Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation

arXiv 2305.15541 ↗First posted 24 May 2023cs.CL cs.AIcited by 59

On the map: LLM alignment / RLHF / preference optimisation → Process reward models for reasoning

Abstract (arXiv)

Translating natural language sentences to first-order logic (NL-FOL translation) is a longstanding challenge in the NLP and formal logic literature. This paper introduces LogicLLaMA, a LLaMA-7B model fine-tuned for NL-FOL translation using LoRA on a single GPU. LogicLLaMA is capable of directly translating natural language into FOL rules, which outperforms GPT-3.5. LogicLLaMA is also equipped to correct FOL rules predicted by GPT-3.5, and can achieve similar performance as GPT-4 with a fraction of the cost. This correction ability was achieved by a novel supervised fine-tuning (SFT) + reinforcement learning with human feedback (RLHF) framework, which initially trains on synthetically perturbed NL-FOL pairs to encourage chain-of-thought reasoning and then fine-tunes with RLHF on GPT-3.5 outputs using a FOL verifier as the reward model. To train LogicLLaMA, we present MALLS (large language Model generAted NL-FOL pairS), a dataset of 34K high-quality and diverse sentence-level NL-FOL pairs collected from GPT-4. The dataset was created by implementing a pipeline that prompts GPT-4 for pairs, and dynamically adjusts the prompts to ensure the collection of pairs with rich and diverse contexts at different levels of complexity, and verifies the validity of the generated FOL rules. Codes, weights, and data are available at hrefhttps://github.com/gblackout/LogicLLaMAsmall https://github.com/gblackout/LogicLLaMA.

Key facts. Cited by 59 papers in the map (data through 14 Oct 2026). Placed in Process reward models for reasoning, one of 10 directions in LLM alignment / RLHF / preference optimisation. Builds on 22 of its 33 references that are in the map. First posted on arXiv 24 May 2023.

Builds on

22 of 33 references.

References · 22

  1. 2023GPT-4 Technical Reportcited by 18,396
  2. 2022Training language models to follow instructions with human feedbackcited by 15,971
  3. 2017Proximal Policy Optimization Algorithmscited by 15,215
  4. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  5. 2023LLaMA: Open and Efficient Foundation Language Modelscited by 14,132
  6. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  7. 2022PaLM: Scaling Language Modeling with Pathwayscited by 5,326
  8. 2023Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoningcited by 391
  9. 2020Generative Language Modeling for Automated Theorem Provingcited by 388
  10. 2020Transformers as Soft Reasoners over Languagecited by 270
  11. 2022FOLIO: Natural Language Reasoning with First-Order Logiccited by 235
  12. 2020ReClor: A Reading Comprehension Dataset Requiring Logical Reasoningcited by 217
10 more
  1. 2020Retrieve, Program, Repeat: Complex Knowledge Base Question Answering via Alternate Meta-learningcited by 216
  2. 2018Learning a SAT Solver from Single-Bit Supervisioncited by 200
  3. 2020NeuroLogic Decoding: (Un)supervised Neural Text Generation with Predicate Logic Constraintscited by 149
  4. 2023SatLM: Satisfiability-Aided Language Models Using Declarative Promptingcited by 102
  5. 2021Improving Coherence and Consistency in Neural Sequence Models with Dual-System, Neuro-Symbolic Reasoningcited by 85
  6. 2021Logic-Driven Context Extension and Data Augmentation for Logical Reasoning of Textcited by 46
  7. 2022Formal Specifications from Natural Languagecited by 33
  8. 2019Semantic Parsing with Dual Learningcited by 28
  9. 2020Exploring Neural Models for Parsing Natural Language into First-Order Logiccited by 16
  10. 2017LangPro: Natural Language Theorem Provercited by 15

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 18; 2025: 18; 2026: 20.

59 papers.

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  1. 2024Large Language Models Can Learn Temporal Reasoningcited by 111
  2. 2024A Survey on LLM-based Code Generation for Low-Resource and Domain-Specific Programming Languagescited by 66
  3. 2023Symbol-LLM: Towards Foundational Symbol-centric Interface For Large Language Modelscited by 39
  4. 2024DELTA: Decomposed Efficient Long-Term Robot Task Planning using Large Language Modelscited by 33
  5. 2024Graph Machine Learning in the Era of Large Language Models (LLMs)cited by 33
  6. 2025Semantic-Aware Logical Reasoning via a Semiotic Frameworkcited by 32
  7. 2026Logical Phase Transitions: Understanding Collapse in LLM Logical Reasoningcited by 25
  8. 2024MedHalu: Hallucinations in Responses to Healthcare Queries by Large Language Modelscited by 21
  9. 2025Frontier LLMs Still Struggle with Simple Reasoning Taskscited by 21
  10. 2023Ontology engineering with Large Language Modelscited by 17
  11. 2025Dissecting Logical Reasoning in LLMs: A Fine-Grained Evaluation and Supervision Studycited by 17
  12. 2025Logic Jailbreak: Efficiently Unlocking LLM Safety Restrictions Through Formal Logical Expressioncited by 16
38 more
  1. 2026ToolGate: Contract-Grounded and Verified Tool Execution for LLMscited by 15
  2. 2024Can LLMs Reason in the Wild with Programs?cited by 13
  3. 2024Beyond Math: Stories as a Testbed for Memorization-Constrained Reasoning in LLMscited by 12
  4. 2023Synergistic Integration of Large Language Models and Cognitive Architectures for Robust AI: An Exploratory Analysiscited by 11
  5. 2024Strategies for Improving NL-to-FOL Translation with LLMs: Data Generation, Incremental Fine-Tuning, and Verificationcited by 10
  6. 2024EventGround: Narrative Reasoning by Grounding to Eventuality-centric Knowledge Graphscited by 9
  7. 2024A Closer Look at Logical Reasoning with LLMs: The Choice of Tool Matterscited by 8
  8. 2025Adaptive LLM-Symbolic Reasoning via Dynamic Logical Solver Compositioncited by 7
  9. 2025Beyond Correctness: Exposing LLM-generated Logical Flaws in Reasoning via Multi-step Automated Theorem Provingcited by 6
  10. 2026PathWise: Planning through World Model for Automated Heuristic Design via Self-Evolving LLMscited by 6
  11. 2025Entailment-Preserving First-order Logic Representations in Natural Language Entailmentcited by 5
  12. 2026NL2LOGIC: AST-Guided Translation of Natural Language into First-Order Logic with Large Language Modelscited by 5
  13. 2024Speak It Out: Solving Symbol-Related Problems with Symbol-to-Language Conversion for Language Modelscited by 4
  14. 2024Can Large Language Models Understand DL-Lite Ontologies? An Empirical Studycited by 4
  15. 2025Assessing the Sensitivity and Alignment of FOL Closeness Metricscited by 4
  16. 2025Do Large Language Models Excel in Complex Logical Reasoning with Formal Language?cited by 4
  17. 2024Graph Generation Powered with LLMs for Boosting Multivariate Time-Series Representation Learningcited by 3
  18. 2024forallutoexistsval: Autonomous Assessment of LLMs in Formal Synthesis and Interpretation Taskscited by 3
  19. 2025Deliberate Planning in Language Models with Symbolic Representationcited by 3
  20. 2026Know Your Limits : On the Faithfulness of LLMs as Solvers and Autoformalizers in Legal Reasoningcited by 3
  21. 2024Know Your Needs Better: Towards Structured Understanding of Marketer Demands with Analogical Reasoning Augmented LLMscited by 2
  22. 2024Towards Automated Knowledge Integration From Human-Interpretable Representationscited by 2
  23. 2024Autonomous Evaluation of LLMs for Truth Maintenance and Reasoning Taskscited by 2
  24. 2025Advancing Natural Language Formalization to First Order Logic with Fine-tuned LLMscited by 2
  25. 2025Do LLMs Really Struggle at NL-FOL Translation? Revealing their Strengths via a Novel Benchmarking Strategycited by 2
  26. 2025Fine-Tuned Large Language Models for Logical Translation: Reducing Hallucinations with Lang2Logiccited by 2
  27. 2026A Balanced Neuro-Symbolic Approach for Commonsense Abductive Logiccited by 2
  28. 2026VeriTrans: Fine-Tuned LLM-Assisted NL-to-PL Translation via a Deterministic Neuro-Symbolic Pipelinecited by 2
  29. 2025LOGICPO: Efficient Translation of NL-based Logical Problems to FOL using LLMs and Preference Optimizationcited by 1
  30. 2025Speaking in Words, Thinking in Logic: A Dual-Process Framework in QA Systemscited by 1
  31. 2025Neurosymbolic Inference On Foundation Models For Remote Sensing Text-to-image Retrieval With Complex Queriescited by 1
  32. 2026Draft-and-Prune: Improving the Reliability of Auto-formalization for Logical Reasoningcited by 1
  33. 2026ReasonSTL: Bridging Natural Language and Signal Temporal Logic via Tool-Augmented Process-Rewarded Learningcited by 1
  34. 2026Fixing FOLIO and MALLS: Verified Annotations and an LLM-assisted Framework to Focus Human Relabelingcited by 1
  35. 2026Semiotic logical hexagon theory for LLM logical reasoningcited by 1
  36. 2024Assistive AI for Augmenting Human Decision-makingcited by 0
  37. 2025MultiPL-MoE: Multi-Programming-Lingual Extension of Large Language Models through Hybrid Mixture-of-Expertscited by 0
  38. 2025A First-Order Logic-Based Alternative to Reward Models in RLHFcited by 0

50 most cited of 59 All 59 (JSON)

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  1. 2025Rosetta-PL: Propositional Logic as a Benchmark for Large Language Model Reasoning
  2. 2023Exploring Self-supervised Logic-enhanced Training for Large Language Models
  3. 2024Autoformalizing Natural Language to First-Order Logic: A Case Study in Logical Fallacy Detection
  4. 2026Improving Symbolic Translation of Language Models for Logical Reasoning
  5. 2026NeuroNL2LTL: A Neurosymbolic Framework for Natural Language Translation of Linear Temporal Logic
  6. 2025R1-T1: Fully Incentivizing Translation Capability in LLMs via Reasoning Learning
  7. 2023Coupling Large Language Models with Logic Programming for Robust and General Reasoning from Text
  8. 2025Reasoning Beyond Limits: Advances and Open Problems for LLMs