LGMT: Logic-Grounded Metamorphic Testing for Evaluating the Reasoning Reliability of LLMs

arXiv cs.AI Papers

Summary

This paper introduces LGMT, a framework that uses first-order logic to generate semantically invariant test cases for evaluating LLM reasoning reliability. Experiments on six LLMs show that LGMT exposes hidden defects missed by static benchmarks, suggesting evaluation should focus on robustness under logical invariance.

arXiv:2605.23965v1 Announce Type: new 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.
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# LGMT: Logic-Grounded Metamorphic Testing for Evaluating the Reasoning Reliability of LLMs
Source: [https://arxiv.org/abs/2605.23965](https://arxiv.org/abs/2605.23965)
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> 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\.

## Submission history

From: Zenghui Zhou \[[view email](https://arxiv.org/show-email/44c8ae13/2605.23965)\] **\[v1\]**Tue, 12 May 2026 18:26:59 UTC \(2,359 KB\)

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