Assessing the Sensitivity and Alignment of FOL Closeness Metrics

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 metrics—NL, FOL, and graph-based— and their alignment with LLM as a judge on FOL evaluation to measure robustness. We introduce operator and text-based perturbations to ground-truth FOL statements to assess metric sensitivity. We then evaluate metric robustness by comparing them against LLMs judgement. 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.