Do LLMs Really Struggle at NL-FOL Translation? Revealing their Strengths via a Novel Benchmarking Strategy

• URL: http://arxiv.org/abs/2511.11816v1
• Date: Fri, 14 Nov 2025 19:11:41 GMT
• Title: Do LLMs Really Struggle at NL-FOL Translation? Revealing their Strengths via a Novel Benchmarking Strategy
• Authors: Andrea Brunello, Luca Geatti, Michele Mignani, Angelo Montanari, Nicola Saccomanno,
• Abstract summary: First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL)<n> converting NL to FOL (NL-FOL translation) has remained a longstanding challenge, for both humans and machines.
• Score: 8.915674937865676
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Due to its expressiveness and unambiguous nature, First-Order Logic (FOL) is a powerful formalism for representing concepts expressed in natural language (NL). This is useful, e.g., for specifying and verifying desired system properties. While translating FOL into human-readable English is relatively straightforward, the inverse problem, converting NL to FOL (NL-FOL translation), has remained a longstanding challenge, for both humans and machines. Although the emergence of Large Language Models (LLMs) promised a breakthrough, recent literature provides contrasting results on their ability to perform NL-FOL translation. In this work, we provide a threefold contribution. First, we critically examine existing datasets and protocols for evaluating NL-FOL translation performance, revealing key limitations that may cause a misrepresentation of LLMs' actual capabilities. Second, to overcome these shortcomings, we propose a novel evaluation protocol explicitly designed to distinguish genuine semantic-level logical understanding from superficial pattern recognition, memorization, and dataset contamination. Third, using this new approach, we show that state-of-the-art, dialogue-oriented LLMs demonstrate strong NL-FOL translation skills and a genuine grasp of sentence-level logic, whereas embedding-centric models perform markedly worse.

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