# Logical Consistency of Large Language Models in Fact-checking

arXiv: https://arxiv.org/abs/2412.16100 · HTML: https://mlsanity.com/paper/2412.16100/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 79 of its 104 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 30 of 79)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Language Models as Knowledge Bases?](https://mlsanity.com/paper/1909.01066/) (2019)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)

## Built on by (most cited first, 15 of 15)

- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [Consistently Simulating Human Personas with Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2511.00222/) (2025)
- [Hallucination to Truth: A Review of Fact-Checking and Factuality Evaluation in Large Language Models](https://mlsanity.com/paper/2508.03860/) (2025)
- [MultiHoax: A Dataset of Multi-hop False-Premise Questions](https://mlsanity.com/paper/2506.00264/) (2025)
- [Auditing Google's AI Overviews and Featured Snippets: A Case Study on Baby Care and Pregnancy](https://mlsanity.com/paper/2511.12920/) (2025)
- [A Survey on Proactive Defense Strategies Against Misinformation in Large Language Models](https://mlsanity.com/paper/2507.05288/) (2025)
- [Beyond Calibration: Do a Typed-Decision Model's Probabilities Obey the Probability Axioms?](https://mlsanity.com/paper/2609.33209/) (2026)
- [Self-Taught Self-Correction for Small Language Models](https://mlsanity.com/paper/2503.08681/) (2025)
- [Explaining Large Language Models with gSMILE](https://mlsanity.com/paper/2505.21657/) (2025)
- [Multimedia Verification Through Multi-Agent Deep Research Multimodal Large Language Models](https://mlsanity.com/paper/2507.04410/) (2025)
- [Investigating Language Model Capabilities to Represent and Process Formal Knowledge: A Preliminary Study to Assist Ontology Engineering](https://mlsanity.com/paper/2509.10249/) (2025)
- [Legal Requirements Translation from Law](https://mlsanity.com/paper/2507.02846/) (2025)
- [Same Question, Different Answers: Evaluating LLM Reliability Beyond Accuracy](https://mlsanity.com/paper/2607.22554/) (2026)
- [Global Consistency Repair for Natural-Language Claim Sets](https://mlsanity.com/paper/2601.13600/) (2026)
- [Towards Annotation-Free Validation of MLLMs: A Vision-Language Logical Consistency Metric](https://mlsanity.com/paper/2605.06201/) (2026)

## Abstract (arXiv)

In recent years, large language models (LLMs) have demonstrated significant success in performing varied natural language tasks such as language translation, question-answering, summarizing, fact-checking, etc. Despite LLMs' impressive ability to generate human-like texts, LLMs are infamous for their inconsistent responses - a meaning-preserving change in the input query results in an inconsistent response and attributes to vulnerabilities of LLMs such as hallucination. Consequently, existing research focuses on simple paraphrasing-based consistency assessment of LLMs, and ignores complex queries that necessitate an even better understanding of logical reasoning by an LLM. Our work therefore addresses the logical inconsistency of LLMs under complex logical queries with primitive logical operators, e.g., negation, conjunction, and disjunction. As a test bed, we consider retrieval-augmented LLMs on a fact-checking task involving propositional logic queries from knowledge graphs (KGs). Our contributions are threefold. Benchmark: We introduce three logical fact-checking datasets over KGs for community development towards logically consistent LLMs. Assessment: We propose consistency measures of LLMs on propositional logic queries and demonstrate that existing LLMs lack logical consistency, especially on complex queries. Improvement: We employ supervised fine-tuning to improve the logical consistency of LLMs on the complex fact-checking task with KG contexts. We have made our source code and benchmarks available.