# LOGICPO: Efficient Translation of NL-based Logical Problems to FOL using LLMs and Preference Optimization

arXiv: https://arxiv.org/abs/2506.18383 · HTML: https://mlsanity.com/paper/2506.18383/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)
- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 16 of 16)

- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [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)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Are Emergent Abilities in Large Language Models just In-Context Learning?](https://mlsanity.com/paper/2309.01809/) (2023)
- [SatLM: Satisfiability-Aided Language Models Using Declarative Prompting](https://mlsanity.com/paper/2305.09656/) (2023)
- [Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation](https://mlsanity.com/paper/2305.15541/) (2023)
- [Ask Me Anything: Free-form Visual Question Answering Based on Knowledge from External Sources](https://mlsanity.com/paper/1511.06973/) (2015)
- [Large Language Models Meet Symbolic Provers for Logical Reasoning Evaluation](https://mlsanity.com/paper/2502.06563/) (2025)
- [Knowledge Base Question Answering: A Semantic Parsing Perspective](https://mlsanity.com/paper/2209.04994/) (2022)
- [Interpretable AMR-Based Question Decomposition for Multi-hop Question Answering](https://mlsanity.com/paper/2206.08486/) (2022)
- [Strategies for Improving NL-to-FOL Translation with LLMs: Data Generation, Incremental Fine-Tuning, and Verification](https://mlsanity.com/paper/2409.16461/) (2024)
- [Open-source Frame Semantic Parsing](https://mlsanity.com/paper/2303.12788/) (2023)

## Built on by (most cited first, 1 of 1)

- [Natural Language to First-Order Logic LLM-based Autoformalization](https://mlsanity.com/paper/2610.12030/) (2026)

## Abstract (arXiv)

Logical reasoning is a key task for artificial intelligence due to it's role in major downstream tasks such as Question Answering, Summarization. Recent methods in improving the reasoning ability of LLMs fall short in correctly converting a natural language reasoning problem to an equivalent logical formulation, which hinders the framework's overall ability to reason. Towards this, we propose to use finetuning on a preference optimization dataset to learn to parse and represent a natural language problem as a whole to a consistent logical program by 1) introducing a new supervised and preference optimization dataset LogicPO, and 2) adopting popular techniques such as Direct Preference Optimization (DPO), Kahneman-Tversky optimization (KTO) to finetune open-source LLMs. Our best model with Phi-3.5 consistently outperforms GPT-3.5-turbo's (8-shot) by producing 10% more logically correct and with 14% less syntax errors. Through the framework and our improved evaluation metrics, we offer a promising direction in improving the logical reasoning of LLMs by better representing them in their logical formulations.