Assessing the Sensitivity and Alignment of FOL Closeness Metrics

• URL: http://arxiv.org/abs/2501.08613v3
• Date: Fri, 05 Sep 2025 06:35:41 GMT
• Title: Assessing the Sensitivity and Alignment of FOL Closeness Metrics
• Authors: Ramya Keerthy Thatikonda, Wray Buntine, Ehsan Shareghi,
• Abstract summary: We study the sensitivity of existing NL-, FOL-, and graph-based metrics to capture differences between a sampled FOL and its corresponding ground-truth.<n>We show that combining metrics enhances both robustness and sensitivity compared to using individual metrics.
• Score: 10.795521518273214
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The recent successful paradigm of solving logical reasoning problems with tool-augmented large language models (LLMs) leverages translation of natural language (NL) statements into First-Order Logic~(FOL) and external theorem provers. However, the correctness of FOL statements, comprising operators and text, often go unverified due to the lack of a reliable evaluation metric for comparing generated and ground-truth FOLs. In this paper, we conduct a comprehensive study on the sensitivity of existing NL-, FOL-, and graph-based metrics to capture differences between a sampled FOL and its corresponding ground-truth. We then measure the alignment between a metric-based ranking of FOL outputs and a strong LLM as-a-judge. To do this, we first apply operator and text-based perturbations to ground-truth FOL statements to assess metric sensitivity. We then evaluate metric robustness by comparing the metrics against LLMs judgment. Our empirical findings highlight a clear oversensitivity in the n-gram metric BLEU for text perturbations. The operator perturbation affects the semantic graph metric Smatch++ for structural changes, and the FOL metric for specific operator changes. We observe a closer alignment between BertScore and LLM judgement, proving the importance of semantic evaluation. Additionally, we show that combining metrics enhances both robustness and sensitivity compared to using individual metrics.

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