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    <abstract>Many real-world questions appear deceptively simple yet implicitly demand two capabilities: (i) systematic coverage of a bounded knowledge universe and (ii) compositional set-based reasoning over that universe, a phenomenon we term “the tip of the iceberg.” We formalize this challenge through two orthogonal dimensions: knowledge width, the cardinality of the required universe, and reasoning depth, the number of compositional set operations. We introduce KnowledgeBerg, a benchmark of 4,800 multiple-choice questions derived from 1,183 enumeration seeds spanning 10 domains and 17 languages, with universes grounded in authoritative sources to ensure reproducibility. Representative open-source LLMs demonstrate severe limitations, achieving only 5.26–36.88 F1 on universe enumeration and 16.00–44.19 accuracy on knowledge-grounded reasoning. Diagnostic analyses reveal three stages of failure: completeness, or missing knowledge; awareness, or failure to identify requirements; and application, or incorrect reasoning execution. This pattern persists across languages and model scales. Although test-time compute and retrieval augmentation yield measurable gains—up to 4.35 and 3.78 points, respectively—substantial gaps remain, exposing limitations in how current LLMs organize structured knowledge and execute compositional reasoning over bounded domains. The dataset is available at https://huggingface.co/datasets/2npc/KnowledgeBerg</abstract>
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%0 Conference Proceedings
%T KnowledgeBerg: Evaluating Systematic Knowledge Coverage and Compositional Reasoning in Large Language Models
%A Zhang, Xiao
%A Meng, Qianru
%A Chen, Yongjian
%A Wang, Yumeng
%A Bos, Johan
%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 zhang-etal-2026-knowledgeberg
%X Many real-world questions appear deceptively simple yet implicitly demand two capabilities: (i) systematic coverage of a bounded knowledge universe and (ii) compositional set-based reasoning over that universe, a phenomenon we term “the tip of the iceberg.” We formalize this challenge through two orthogonal dimensions: knowledge width, the cardinality of the required universe, and reasoning depth, the number of compositional set operations. We introduce KnowledgeBerg, a benchmark of 4,800 multiple-choice questions derived from 1,183 enumeration seeds spanning 10 domains and 17 languages, with universes grounded in authoritative sources to ensure reproducibility. Representative open-source LLMs demonstrate severe limitations, achieving only 5.26–36.88 F1 on universe enumeration and 16.00–44.19 accuracy on knowledge-grounded reasoning. Diagnostic analyses reveal three stages of failure: completeness, or missing knowledge; awareness, or failure to identify requirements; and application, or incorrect reasoning execution. This pattern persists across languages and model scales. Although test-time compute and retrieval augmentation yield measurable gains—up to 4.35 and 3.78 points, respectively—substantial gaps remain, exposing limitations in how current LLMs organize structured knowledge and execute compositional reasoning over bounded domains. The dataset is available at https://huggingface.co/datasets/2npc/KnowledgeBerg
%R 10.18653/v1/2026.findings-acl.548
%U https://aclanthology.org/2026.findings-acl.548/
%U https://doi.org/10.18653/v1/2026.findings-acl.548
%P 11272-11286

Markdown (Informal)

[KnowledgeBerg: Evaluating Systematic Knowledge Coverage and Compositional Reasoning in Large Language Models](https://aclanthology.org/2026.findings-acl.548/) (Zhang et al., Findings 2026)

• KnowledgeBerg: Evaluating Systematic Knowledge Coverage and Compositional Reasoning in Large Language Models (Zhang et al., Findings 2026)

ACL

• Xiao Zhang, Qianru Meng, Yongjian Chen, Yumeng Wang, and Johan Bos. 2026. KnowledgeBerg: Evaluating Systematic Knowledge Coverage and Compositional Reasoning in Large Language Models. In Findings of the Association for Computational Linguistics: ACL 2026, pages 11272–11286, San Diego, California, United States. Association for Computational Linguistics.