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This research introduces LGMT, an oracle-free evaluation framework that uses first-order logic to detect hidden reasoning defects in LLMs that static benchmarks miss. The study reveals that current models remain fragile to symbol-level variations and that advanced prompting techniques only partially address these robustness issues. For technical audiences, the key takeaway is the necessity of shifting from isolated correctness checks to assessing robustness under logical invariance for reliable deployment.
LGMT: Logic-Grounded Metamorphic Testing for Evaluating the Reasoning Reliability of LLMs
arXiv:2605.23965v2 Announce Type: replace-cross Abstract: Large Language Models (LLMs) achieve strong performance on logical reasoning benchmarks, yet their reliability remains uncertain. Existing evaluations rely on static benchmarks, which fail to assess robustness under logically equivalent transformations and often overestimate reasoning capability. We propose LGMT (Logic-Grounded Metamorphic Testing), an oracle-free framework that leverages first-order logic (FOL) to evaluate LLM reasoning. By deriving metamorphic relations from formal logical equivalences, LGMT constructs semantically invariant test cases and detects reasoning defects through cross-case consistency checking. Experiments on six state-of-the-art LLMs show that LGMT exposes substantial hidden defects missed by traditional reference-based evaluations. We further find that models are particularly sensitive to symbol-level and conclusion-level variations, and that advanced prompting such as Few-shot CoT only partially mitigates these issues. These results suggest that LLM evaluation should move beyond isolated correctness toward robustness under logical invariance. LGMT provides a principled and scalable approach for diagnosing reasoning failures.
Abstract:Large Language Models (LLMs) achieve strong performance on logical reasoning benchmarks, yet their reliability remains uncertain. Existing evaluations rely on static benchmarks, which fail to assess robustness under logically equivalent transformations and often overestimate reasoning capability. We propose LGMT (Logic-Grounded Metamorphic Testing), an oracle-free framework that leverages first-order logic (FOL) to evaluate LLM reasoning. By deriving metamorphic relations from formal logical equivalences, LGMT constructs semantically invariant test cases and detects reasoning defects through cross-case consistency checking. Experiments on six state-of-the-art LLMs show that LGMT exposes substantial hidden defects missed by traditional reference-based evaluations. We further find that models are particularly sensitive to symbol-level and conclusion-level variations, and that advanced prompting such as Few-shot CoT only partially mitigates these issues. These results suggest that LLM evaluation should move beyond isolated correctness toward robustness under logical invariance. LGMT provides a principled and scalable approach for diagnosing reasoning failures.
Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Software Engineering (cs.SE)
arXiv:2605.23965 [cs.AI]
(or arXiv:2605.23965v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2605.23965 Focus to learn more arXiv-issued DOI via DataCite
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