# When Absence Is Evidence: Evaluating Completeness-Sensitive Negative Reasoning in Large Language Models

arXiv: https://arxiv.org/abs/2608.04591 · HTML: https://mlsanity.com/paper/2608.04591/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 3 of its 31 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 3 of 3)

- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [AbstentionBench: Reasoning LLMs Fail on Unanswerable Questions](https://mlsanity.com/paper/2506.09038/) (2025)
- [AbsenceBench: Language Models Can't Tell What's Missing](https://mlsanity.com/paper/2506.11440/) (2025)

## Built on by (most cited first, 1 of 1)

- [Coding Agents Aren't Enough! Evaluating an Enterprise Security Brain for Agentic Cloud Investigations](https://mlsanity.com/paper/2609.30345/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are often asked whether something is absent from a record, list, or retrieved context. Yet non-observation licenses a negative answer only when evidence completely covers the query scope; otherwise, the answer should remain unknown. We call this completeness-sensitive negative reasoning. We introduce CROWN-QA, comprising CROWN-Synth, a controlled paired core that fixes the question and observed facts while varying only query-relative coverage, and CROWN-Real, a real-document contrast-set evaluation with controlled coverage variants. Across three LLM families, models show unstable closure judgments and substantial over-closure, failing to reliably distinguish a justified negative answer (Certified-Negative) from insufficient evidence (Unknown). The dominant CROWN-Synth failure is asymmetric: models often recognize implicitly complete evidence yet treat implicitly partial evidence as query-covering. Prompting redistributes errors between over- and under-closure rather than consistently resolving them. Structured certificate elicitation traces many errors to evidence-coverage mischaracterization. CROWN-Real shows that the core partial-coverage asymmetry persists on real-document content, while its strength and the balance between over- and under-closure vary by model, prompt, and source.