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QMFOL: Benchmarking Large Language Model Reasoning... | AI Research

Key Takeaways

  • QMFOL: Benchmarking Large Language Model Reasoning via Quantifiable Monadic First-Order Logic Test Case Generation As Large Language Models (LLMs) continue t...
  • Large Language Models (LLMs) have made significant progress in reasoning, particularly in deductive reasoning, which is crucial for high-stakes decision-making.
  • As models improve, evaluation benchmarks should evolve to keep pace.
  • However, existing benchmarks lack fine-grained control over logical complexity and struggle to balance semantic diversity with logical consistency.
  • To address these issues, we propose QMFOL, an automated framework for generating monadic first-order logic reasoning tasks with quantifiable and controllable complexity.
Paper AbstractExpand

Large Language Models (LLMs) have made significant progress in reasoning, particularly in deductive reasoning, which is crucial for high-stakes decision-making. As models improve, evaluation benchmarks should evolve to keep pace. However, existing benchmarks lack fine-grained control over logical complexity and struggle to balance semantic diversity with logical consistency. To address these issues, we propose QMFOL, an automated framework for generating monadic first-order logic reasoning tasks with quantifiable and controllable complexity. It constructs formal logical structures using conjunction and disjunction patterns, enabling precise control over reasoning depth, width, label types, and distractors. These structures are then translated into natural language via LLMs, with logical consistency ensured through round-trip verification using an external prover. Based on our framework, we build QMFOLBench, a benchmark comprising 2880 instances with 960 configurations across diverse logical and semantic dimensions. Evaluations on six large reasoning models (LRMs) and two LLMs show that performance degrades and computational overhead increases with rising logical complexity. Models perform better on True-labeled tasks than on False or Unknown ones, and exhibit sensitivity to semantic variation. Overall, QMFOL offers a scalable and reliable approach for constructing deductive reasoning benchmarks with controllable complexity, enabling more precise evaluation of reasoning capabilities in modern language models.

QMFOL: Benchmarking Large Language Model Reasoning via Quantifiable Monadic First-Order Logic Test Case Generation
As Large Language Models (LLMs) continue to advance, their ability to perform deductive reasoning—the process of drawing logical conclusions from established premises—has become essential for high-stakes fields like law and healthcare. However, current evaluation methods struggle to measure these capabilities precisely. Existing benchmarks often lack the ability to control logical complexity, and they frequently face a trade-off between being easy to generate and maintaining logical accuracy. This paper introduces QMFOL, an automated framework designed to create highly controllable, logically consistent reasoning tasks to better evaluate how modern models handle complex, multi-step deduction.

A Scalable Framework for Logical Complexity

The QMFOL framework addresses the need for fine-grained control by using Monadic First-Order Logic (MFOL). By restricting predicates to a unary form, the researchers can systematically manipulate the "depth" and "width" of logical structures. Depth refers to the number of inference steps, while width relates to the complexity of the logical connectives (such as "and" or "or") within those steps. The framework also allows for the insertion of "distractor" rules—extra information that mimics real-world scenarios but does not affect the logical outcome—to test how well models can filter out irrelevant data.

Ensuring Logical Consistency

A major challenge in creating reasoning benchmarks is ensuring that the natural language versions of these tasks remain logically sound. QMFOL solves this by using a two-step process. First, it constructs a formal logical structure. Second, it uses an LLM to translate that structure into natural language based on specific topics like animals or mathematics. To guarantee that the meaning remains unchanged during this translation, the framework performs "round-trip verification": it translates the natural language back into formal logic and uses an external prover to ensure the final output matches the original, intended logical structure.

Insights from QMFOLBench

Using this framework, the authors built QMFOLBench, a dataset containing 2,880 instances across 960 different configurations. When testing various reasoning models, the researchers observed several key trends:

  • Complexity Impacts Performance: As the logical depth and width of the tasks increased, model accuracy consistently declined, and the computational effort required to solve the problems rose.

  • Label Sensitivity: Models generally performed better on tasks where the correct answer was "True" compared to those labeled "False" or "Unknown." * Semantic Dependence: Even when the underlying logical structure was identical, model performance varied depending on the topic, suggesting that models are sensitive to the specific semantic context of the reasoning task.

Why This Matters

By providing a way to generate tasks with quantifiable difficulty, QMFOL offers a more reliable and scalable approach to benchmarking. Instead of relying on static datasets that may become contaminated by training data, this framework allows researchers to generate new, controlled test cases on demand. This enables a more precise understanding of where current models excel and where they struggle, ultimately supporting the development of more robust and reliable reasoning capabilities in future AI systems.

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