@inproceedings{bi-etal-2026-logical,
    title = "Logical Structure as Knowledge: Enhancing {LLM} Reasoning via Structured Logical Knowledge Density Estimation",
    author = "Bi, Zhen  and
      Hu, Zhenlin  and
      Chen, Xueshu  and
      Chen, Mingyang  and
      Deng, Cheng  and
      Xue, Yida  and
      Wang, Zhen  and
      Shen, Qing  and
      Zhang, Ningyu  and
      Lou, Jungang",
    editor = "Liakata, Maria  and
      Moreira, Viviane P.  and
      Zhang, Jiajun  and
      Jurgens, David",
    booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
    month = jul,
    year = "2026",
    address = "San Diego, California, United States",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingest-acl/2026.findings-acl.436/",
    pages = "8978--8999",
    ISBN = "979-8-89176-395-1",
    abstract = "The reasoning capabilities of Large Language Models (LLMs) are increasingly attributed to training data quality rather than mere parameter scaling. However, existing data-centric paradigms often equate quality with factuality or diversity and ignore the internal logical complexity of training samples. In this work, we propose that natural language harbors Structured Logical Knowledge manifested through entailment relationships and logical topologies. To quantify this, we introduce Structured Logical Knowledge Density (SLKD), a novel metric that measures logical information content by decomposing natural language into executable predicates and logical primitives. Our analysis reveals a significant logical disparity in current datasets where sparse logical signals predominate. Consequently, we propose a density-aware re-cognizing optimization strategy that prioritizes high-density logical samples to align training with the model{'}s reasoning boundary. Extensive experiments demonstrate that our approach enhances reasoning performance and generalization without increasing total data volume. These results, further validated within a reinforcement learning framework, suggest that elevating logical density is more critical than expanding data scale for realizing the full cognitive potential of LLMs. The anonymized code is available in the Appendix C."
}