---
title: "Logical Consistency as a Bridge — paper by Mi et al. (2026)"
description: "The authors propose LaaB (Logical Consistency-as-a-Bridge), which combines both. 77 references."
authors: ["Hao Mi", "Qiang Sheng", "Shaofei Wang", "Beizhe Hu", "Yifan Sun", "Zhengjia Wang", "Hengqi Zeng", "Yang Li", "Danding Wang", "Juan Cao"]
year: 2026
venue: "Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)"
source: "https://aclanthology.org/2026.acl-long.286/"
doi: "10.18653/v1/2026.acl-long.286"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/mi-2026-logical-consistency-as-bridge-improving/"
---
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# Logical Consistency as a Bridge: Improving LLM Hallucination Detection via Label Constraint Modeling between Responses and Self-Judgments

**Authors:** Hao Mi, [Qiang Sheng](https://md.research.elamur.ai/free/en/authors/qiang-sheng/), Shaofei Wang, [Beizhe Hu](https://md.research.elamur.ai/free/en/authors/beizhe-hu/), [Yifan Sun](https://md.research.elamur.ai/free/en/authors/yifan-sun/), Zhengjia Wang, Hengqi Zeng, [Yang Li](https://md.research.elamur.ai/free/en/authors/yang-li/), [Danding Wang](https://md.research.elamur.ai/free/en/authors/danding-wang/) and [Juan Cao](https://md.research.elamur.ai/free/en/authors/juan-cao/) · **Year:** 2026 · **Venue:** [Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2026](https://md.research.elamur.ai/free/en/venues/acl/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.acl-long.286/) · [PDF](https://aclanthology.org/2026.acl-long.286.pdf) · [DOI 10.18653/v1/2026.acl-long.286](https://doi.org/10.18653/v1/2026.acl-long.286) · [OpenAlex](https://openalex.org/W7166867317)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary
The paper tackles factual hallucination detection in LLMs, framed as binary classification of whether a response is factual. Existing detectors follow one of two routes. Some read internal signals such as hidden states or logits, which can miss confidently wrong answers. Others prompt the model to judge itself, which inherits self-preference bias. The authors propose LaaB (Logical Consistency-as-a-Bridge), which combines both. The model's own Yes/No verdict on its answer is treated as just another generation that might be hallucinated, so a second detector analyzes the internal features of that verdict (a "meta-judgment"). The two views are linked by a simple rule: a "Yes" verdict means the answer and the verdict share the same factuality label, while a "No" means the labels are opposite. The two detectors are trained jointly through logic-constrained mutual learning. Experiments use TriviaQA, MMLU, NQ_Open and HaluEval with four open-source LLMs and eight baselines. LaaB improves detection for most base models while adding little inference cost. This makes it practical for LLM providers who want to monitor their own services.

## Key points
- **Architecture:** a response detector D_r works on intrinsic features of the answer, and a judgment detector D_j works on intrinsic features of the self-judgment. The judgment detector's prediction is kept for "Yes" and flipped (1 − S_j) for "No". The two predictions are aligned with a Huber-based logic loss alongside cross-entropy. D_j is discarded after training.
- **Evaluation setup:** 4 public datasets (TriviaQA, MMLU, NQ_Open, HaluEval), 4 LLMs and 8 baselines. Code and data are released at github.com/ICTMCG/LaaB.
- **Error analysis:** a Sankey analysis shows that many of D_r's earlier errors become correct while most of its correct predictions are preserved. A few cases that both views originally got wrong are also fixed.
- **Effect of length:** gains are largest for longer responses, peaking on MMLU instances longer than 30 tokens.
- **Limitations:**
  - Forcing a Yes/No answer may add noise.
  - The logic constraint is soft, so consistency is not guaranteed for every sample.
  - The method needs white-box access to the LLM, so it suits providers rather than third parties.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Chinese Academy of Sciences](https://md.research.elamur.ai/free/en/government/chinese-academy-of-sciences/) — Government body, Beijing, China · 194 works · 23,906 citations
- [University of Chinese Academy of Sciences](https://md.research.elamur.ai/free/en/universities/university-of-chinese-academy-of-sciences/) — University, Beijing, China · 147 works · 8,480 citations
- [Institute of Computing Technology](https://md.research.elamur.ai/free/en/labs/institute-of-computing-technology/) — Research institute, Beijing, China · 51 works · 3,411 citations

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## Cite

Cite as: Hao Mi, Qiang Sheng, Shaofei Wang, Beizhe Hu, Yifan Sun, Zhengjia Wang, Hengqi Zeng, Yang Li, Danding Wang and Juan Cao. 2026. Logical Consistency as a Bridge: Improving LLM Hallucination Detection via Label Constraint Modeling between Responses and Self-Judgments. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{mi2026logical,
  title = {{Logical Consistency as a Bridge: Improving LLM Hallucination Detection via Label Constraint Modeling between Responses and Self-Judgments}},
  author = {Hao Mi, Qiang Sheng, Shaofei Wang, Beizhe Hu, Yifan Sun, Zhengjia Wang, Hengqi Zeng, Yang Li, Danding Wang and Juan Cao},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.286},
  url = {https://doi.org/10.18653/v1/2026.acl-long.286}
}
```

- [← previous Logic-Level Evaluation of Logical Table-to-Text Generation](https://md.research.elamur.ai/free/en/papers/trigg-2026-logic-level-evaluation-logical-table/)
- [next → LogicEval: A Systematic Framework for Evaluating Automated Repair Techniques for Logical Vulnerabilities in Real-World Software](https://md.research.elamur.ai/free/en/papers/rashid-2026-logiceval-systematic-framework-evaluating-automated/)
- [↑ back to papers of 2026](https://md.research.elamur.ai/free/en/papers/2026/page/35/)

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*Updated 1 November 2026*
