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

Open-domain semantic parsing remains a challenging task, as neural models often rely on heuristics and struggle to handle unseen concepts. In this paper, we investigate the potential of large language models (LLMs) for this task and introduce Retrieval-Augmented Semantic Parsing (RASP), a simple yet effective approach that integrates external symbolic knowledge into the parsing process. Our experiments not only show that LLMs outperform previous encoder-decoder baselines for semantic parsing, but that RASP further enhances their ability to predict unseen concepts, nearly doubling the performance of previous models on out-of-distribution concepts. These findings highlight the promise of leveraging large language models and retrieval mechanisms for robust and open-domain semantic parsing.