# Global Consistency Repair for Natural-Language Claim Sets

arXiv: https://arxiv.org/abs/2601.13600 · HTML: https://mlsanity.com/paper/2601.13600/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Builds on (most cited first, 19 of 19)

- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Evaluating the Factual Consistency of Abstractive Text Summarization](https://mlsanity.com/paper/1910.12840/) (2019)
- [LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods](https://mlsanity.com/paper/2412.05579/) (2024)
- [A Survey on Automated Fact-Checking](https://mlsanity.com/paper/2108.11896/) (2021)
- [Get Your Vitamin C! Robust Fact Verification with Contrastive Evidence](https://mlsanity.com/paper/2103.08541/) (2021)
- [Fact-Checking Complex Claims with Program-Guided Reasoning](https://mlsanity.com/paper/2305.12744/) (2023)
- [Automated Fact Checking: Task formulations, methods and future directions](https://mlsanity.com/paper/1806.07687/) (2018)
- [Explainable Claim Verification via Knowledge-Grounded Reasoning with Large Language Models](https://mlsanity.com/paper/2310.05253/) (2023)
- [Decomposition Dilemmas: Does Claim Decomposition Boost or Burden Fact-Checking Performance?](https://mlsanity.com/paper/2411.02400/) (2024)
- [Logical Consistency of Large Language Models in Fact-checking](https://mlsanity.com/paper/2412.16100/) (2024)
- [Halu-J: Critique-Based Hallucination Judge](https://mlsanity.com/paper/2407.12943/) (2024)
- [GraphCheck: Breaking Long-Term Text Barriers with Extracted Knowledge Graph-Powered Fact-Checking](https://mlsanity.com/paper/2502.16514/) (2025)
- [Natural Logic-guided Autoregressive Multi-hop Document Retrieval for Fact Verification](https://mlsanity.com/paper/2212.05276/) (2022)
- [MetaSumPerceiver: Multimodal Multi-Document Evidence Summarization for Fact-Checking](https://mlsanity.com/paper/2407.13089/) (2024)
- [ConsistencyChecker: Tree-based Evaluation of LLM Generalization Capabilities](https://mlsanity.com/paper/2506.12376/) (2025)

## Abstract (arXiv)

NLP systems increasingly aggregate claims from retrieved passages, documents, and generated reasoning steps. Yet current factuality methods mostly verify claims individually or compare pairs of claims, leaving open the question of whether the entire aggregated claim set can be retained coherently. This misses a fundamental failure mode: claims may be locally plausible and pairwise compatible while still being jointly inconsistent. We formalize global consistency repair: given an inconsistent natural-language claim set, preserve the largest coherent subset while localizing the compact sources of inconsistency. We introduce QXR, an adaptive diagnosis-and-repair framework that treats an LLM as a noisy set-level consistency judge, localizes minimal conflicting subsets, and repairs the claim set by deleting a small hitting set of claims. Across LLM judges and benchmarks derived from VitaminC, FEVER, and conflicting-evidence RAG, QXR preserves substantially more valid claims than direct all-at-once judging while maintaining high precision. These results suggest that factuality in claim aggregation systems should be treated as a set-level repair problem, not only as local verification.