# Entailment-Preserving First-order Logic Representations in Natural Language Entailment

arXiv: https://arxiv.org/abs/2502.16757 · HTML: https://mlsanity.com/paper/2502.16757/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 24 Feb 2025.

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

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [e-SNLI: Natural Language Inference with Natural Language Explanations](https://mlsanity.com/paper/1812.01193/) (2018)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [QASC: A Dataset for Question Answering via Sentence Composition](https://mlsanity.com/paper/1910.11473/) (2019)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [BRIO: Bringing Order to Abstractive Summarization](https://mlsanity.com/paper/2203.16804/) (2022)
- [Explaining Answers with Entailment Trees](https://mlsanity.com/paper/2104.08661/) (2021)
- [Minimum Risk Training for Neural Machine Translation](https://mlsanity.com/paper/1512.02433/) (2015)
- [Multi-shot ASP solving with clingo](https://mlsanity.com/paper/1705.09811/) (2017)
- [Building Math Agents with Multi-Turn Iterative Preference Learning](https://mlsanity.com/paper/2409.02392/) (2024)
- [Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation](https://mlsanity.com/paper/2305.15541/) (2023)
- [Graph Pre-training for AMR Parsing and Generation](https://mlsanity.com/paper/2203.07836/) (2022)
- [Learning to Explain: Datasets and Models for Identifying Valid Reasoning Chains in Multihop Question-Answering](https://mlsanity.com/paper/2010.03274/) (2020)
- [Divide and Translate: Compositional First-Order Logic Translation and Verification for Complex Logical Reasoning](https://mlsanity.com/paper/2410.08047/) (2024)
- [Learning an Executable Neural Semantic Parser](https://mlsanity.com/paper/1711.05066/) (2017)
- [Weakly-supervised Neural Semantic Parsing with a Generative Ranker](https://mlsanity.com/paper/1808.07625/) (2018)

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

- [Logic Jailbreak: Efficiently Unlocking LLM Safety Restrictions Through Formal Logical Expression](https://mlsanity.com/paper/2505.13527/) (2025)
- [A framework for auditing grounding claims](https://mlsanity.com/paper/2512.06205/) (2025)
- [Technical Report -- A Context-Sensitive Multi-Level Similarity Framework for First-Order Logic Arguments: An Axiomatic Study](https://mlsanity.com/paper/2604.12534/) (2026)
- [Quizzing the Translation: A Prover-Grounded Evaluation Metric for NLrightarrowFOL](https://mlsanity.com/paper/2609.33612/) (2026)
- [Learning Proposition-Level Links from Sentence-Level Supervision for Neuro-Symbolic NLI](https://mlsanity.com/paper/2610.15158/) (2026)

## Abstract (arXiv)

First-order logic (FOL) can represent the logical entailment semantics of natural language (NL) sentences, but determining natural language entailment using FOL remains a challenge. To address this, we propose the Entailment-Preserving FOL representations (EPF) task and introduce reference-free evaluation metrics for EPF, the Entailment-Preserving Rate (EPR) family. In EPF, one should generate FOL representations from multi-premise natural language entailment data (e.g. EntailmentBank) so that the automatic prover's result preserves the entailment labels. Experiments show that existing methods for NL-to-FOL translation struggle in EPF. To this extent, we propose a training method specialized for the task, iterative learning-to-rank, which directly optimizes the model's EPR score through a novel scoring function and a learning-to-rank objective. Our method achieves a 1.8-2.7% improvement in EPR and a 17.4-20.6% increase in EPR@16 compared to diverse baselines in three datasets. Further analyses reveal that iterative learning-to-rank effectively suppresses the arbitrariness of FOL representation by reducing the diversity of predicate signatures, and maintains strong performance across diverse inference types and out-of-domain data.