When Form Changes but Logic Doesn't: Building Logic-invariant LLMs through Logical Structure

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.

Large language models (LLMs) frequently contradict themselves when the surface form of a logically equivalent question changes. We present a benchmark of 350 question families (1,750 total questions) for Controlled Reformulation Testing (CRTBench) to evaluate logical invariance. In this benchmark, we investigate LLMs' ability to maintain consistent answers across controlled reformulations, which include contrapositive rewriting, double negation, negation flipping, and passive voice. We evaluate several frontier LLMs and observe an accuracy-consistency gap where GPT-5.4-mini achieves $98.9\%$ base accuracy but only $60.3\%$ family-level consistency, while reasoning-optimized o4-mini achieves $96.9\%$ consistency. From our experiments, we observe that failures cluster around logically nontrivial transformations such as contrapositive rewriting ($72.4\%$ for GPT-5.4-mini) and double negation ($84.6\%$), while surface-level rephrasing remains robust ($94-100\%$). Increasing reasoning effort improves GPT-5.4-mini to $85.4\%$ consistency, but leaves GPT-5.4 unchanged overall because gains on nested negation are offset by failures on quantifier families. These results show that accuracy alone is not enough for evaluating logical reasoning in LLMs.

Logical reasoning with large language models (LLMs) is a critical capability, as it reflects a system's ability to correctly deduce hypotheses from a given context using faithful deductive processes. However, LLM reasoning has often been shown to be sensitive to small surface-level variations in problem formulation, raising questions about whether models truly follow the underlying logical structure. Studying this behavior is challenging because the symbolic components of logical problems, such as operators and predicates, are difficult to systematically manipulate in natural language. We introduce a tool-driven framework for generating controlled, label-preserving edits to logical reasoning problems. Our method operates on symbolic representations of first-order logic and constraint satisfaction problem tasks, enabling targeted modifications to logical operators and other structural components before translating them back into natural language. Using this framework, we evaluate various LLMs under cumulative and individual operator edits and analyze their behavior in response to these changes. Our quantitative and qualitative analyses show that LLM reasoning behavior under controlled operator edits is inconsistent, regardless of model size or family: models sometimes adapt correctly to structural changes but often fail to track their logical consequences. The results from this automated stress test enable an evaluation of language models across different dimensions and help measure the reliability of their reasoning.