@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://aclanthology.org/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."
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<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.</abstract>
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%0 Conference Proceedings
%T Logical Structure as Knowledge: Enhancing LLM Reasoning via Structured Logical Knowledge Density Estimation
%A Bi, Zhen
%A Hu, Zhenlin
%A Chen, Xueshu
%A Chen, Mingyang
%A Deng, Cheng
%A Xue, Yida
%A Wang, Zhen
%A Shen, Qing
%A Zhang, Ningyu
%A Lou, Jungang
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F bi-etal-2026-logical
%X 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.
%U https://aclanthology.org/2026.findings-acl.436/
%P 8978-8999
Markdown (Informal)
[Logical Structure as Knowledge: Enhancing LLM Reasoning via Structured Logical Knowledge Density Estimation](https://aclanthology.org/2026.findings-acl.436/) (Bi et al., Findings 2026)
ACL
- Zhen Bi, Zhenlin Hu, Xueshu Chen, Mingyang Chen, Cheng Deng, Yida Xue, Zhen Wang, Qing Shen, Ningyu Zhang, and Jungang Lou. 2026. Logical Structure as Knowledge: Enhancing LLM Reasoning via Structured Logical Knowledge Density Estimation. In Findings of the Association for Computational Linguistics: ACL 2026, pages 8978–8999, San Diego, California, United States. Association for Computational Linguistics.