# Fine-Tuned Large Language Models for Logical Translation: Reducing Hallucinations with Lang2Logic

arXiv: https://arxiv.org/abs/2512.02987 · HTML: https://mlsanity.com/paper/2512.02987/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 4 of 4)

- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation](https://mlsanity.com/paper/2305.15541/) (2023)
- [SATBench: Benchmarking LLMs' Logical Reasoning via Automated Puzzle Generation from SAT Formulas](https://mlsanity.com/paper/2505.14615/) (2025)

## Built on by (most cited first, 2 of 2)

- [TIAR: Trajectory-Informed Advantage Reweighting for LLM Abstention Learning](https://mlsanity.com/paper/2605.25850/) (2026)
- [VeriTrans: Fine-Tuned LLM-Assisted NL-to-PL Translation via a Deterministic Neuro-Symbolic Pipeline](https://mlsanity.com/paper/2604.10341/) (2026)

## Abstract (arXiv)

Recent advances in natural language processing (NLP), particularly large language models (LLMs), have motivated the automatic translation of natural language statements into formal logic without human intervention. This enables automated reasoning and facilitates debugging, finding loop invariants, and adhering to specifications in software systems. However, hallucinations-incorrect outputs generated by LLMs are challenging, particularly for logical translation tasks requiring precision. This work introduces a novel framework that inputs English sentences, converts them into logical expressions, and then translates them into Conjunctive Normal Form (CNF) for satisfiability solving. It employs classical NLP techniques with self-defined grammar, symbolic computation libraries, and a fine-tuned language model to reduce hallucinations. In the early experiments, we observed that the fine-tuned model, trained on different grammar settings, could intentionally correct the same types of hallucinations made by the original model. Thus, it provides reliable CNF generation.