Assessing the Alignment of FOL Closeness Metrics with Human Judgement

The recent successful paradigm of solving logical reasoning problems with tool-augmented large language models (LLMs) leverages translation of natural language statements into First-Order Logic~(FOL) and external theorem provers. However, the correctness of FOL statements, comprising operators and text predicates, often goes unverified due to the lack of a reliable evaluation metric for comparing generated and ground-truth FOLs. In this paper, we present a comprehensive study of sensitivity of existing metrics and their alignment with human judgement on FOL evaluation. Using ground-truth FOLs, we carefully designed various perturbations on the ground-truth to assess metric sensitivity. We sample FOL translation candidates for natural language statements and measure the ranking alignment between automatic metrics and human annotators. Our empirical findings highlight oversensitivity in the n-gram metric BLEU for text perturbations, the semantic graph metric Smatch++ for structural perturbations, and FOL metric for operator perturbation. We also observe a closer alignment between BertScore and human judgement. Additionally, we show that combining metrics enhances both alignment and sensitivity compared to using individual metrics.