# Neither True nor False: Do LLMs Represent Truth-Value Gaps in Plural Predication?

arXiv: https://arxiv.org/abs/2610.14438 · HTML: https://mlsanity.com/paper/2610.14438/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 14 of 14)

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- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [ChatGLM: A Family of Large Language Models from GLM-130B to GLM-4 All Tools](https://mlsanity.com/paper/2406.12793/) (2024)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [BLiMP: The Benchmark of Linguistic Minimal Pairs for English](https://mlsanity.com/paper/1912.00582/) (2019)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [What BERT is not: Lessons from a new suite of psycholinguistic diagnostics for language models](https://mlsanity.com/paper/1907.13528/) (2019)
- [Negated and Misprimed Probes for Pretrained Language Models: Birds Can Talk, But Cannot Fly](https://mlsanity.com/paper/1911.03343/) (2019)
- [Are Natural Language Inference Models IMPPRESsive? Learning IMPlicature and PRESupposition](https://mlsanity.com/paper/2004.03066/) (2020)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly being used to summarize and verify claims in critical sources that inform consequential decisions. Such claims are full of plural definites. If three of five patients improved after taking drug A, the claim the patients improved after drug A is not true, since two did not, yet its negation, the patients didn't improve after drug A, is not true either, since three did. In formal semantics, this truth-value gap is known as the Homogeneity Gap: both the plural definite and its negation are neither true nor false when the property holds for only a fraction of the plural referent. A model that cannot represent this gap turns mixed evidence into a clean verdict, an error that can be costly in high-stakes use. We introduce HomogeneityNLI, a diagnostic dataset of 1,000 minimal pair items crossing determiner, polarity, and group composition across ten logical conditions. Evaluating seven open-weight models, we uncover a pervasive Bivalence Bias: models assign plural definites their homogeneous truth conditions. In the zero-shot setting, no model recognizes the gap for both polarities in more than 15% of scenarios, and negated definites are judged False in 84% of cases. Explicit linguistic rules, chain-of-thought, and enumeration prompts produce unstable, model-specific effects that often entrench the bias. Our findings indicate that current open-weight LLMs acquire the truth conditions of plural predication but not its trivalent logic, and cannot yet be trusted to summarize or verify claims whose evidence is mixed.