# Position: Logical Soundness is not a Reliable Criterion for Neurosymbolic Fact-Checking with LLMs

arXiv: https://arxiv.org/abs/2604.04177 · HTML: https://mlsanity.com/paper/2604.04177/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 52 references that are in the map.
- First posted on arXiv 5 Apr 2026.

## Builds on (most cited first, 30 of 36)

- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [A Survey on Automated Fact-Checking](https://mlsanity.com/paper/2108.11896/) (2021)
- [Can LLM-Generated Misinformation Be Detected?](https://mlsanity.com/paper/2309.13788/) (2023)
- [Fact-Checking Complex Claims with Program-Guided Reasoning](https://mlsanity.com/paper/2305.12744/) (2023)
- [Factuality Challenges in the Era of Large Language Models](https://mlsanity.com/paper/2310.05189/) (2023)
- [LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models](https://mlsanity.com/paper/2404.15522/) (2024)
- [A Survey of Uncertainty Estimation Methods on Large Language Models](https://mlsanity.com/paper/2503.00172/) (2025)
- [ProoFVer: Natural Logic Theorem Proving for Fact Verification](https://mlsanity.com/paper/2108.11357/) (2021)
- [Multimodal Automated Fact-Checking: A Survey](https://mlsanity.com/paper/2305.13507/) (2023)
- [Towards Reliable Misinformation Mitigation: Generalization, Uncertainty, and GPT-4](https://mlsanity.com/paper/2305.14928/) (2023)
- [GenAI Against Humanity: Nefarious Applications of Generative Artificial Intelligence and Large Language Models](https://mlsanity.com/paper/2310.00737/) (2023)
- [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)
- [The Perils & Promises of Fact-checking with Large Language Models](https://mlsanity.com/paper/2310.13549/) (2023)
- [Large Language Models Portray Socially Subordinate Groups as More Homogeneous, Consistent with a Bias Observed in Humans](https://mlsanity.com/paper/2401.08495/) (2024)
- [Pragmatics in the Era of Large Language Models: A Survey on Datasets, Evaluation, Opportunities and Challenges](https://mlsanity.com/paper/2502.12378/) (2025)
- [Logically Consistent Language Models via Neuro-Symbolic Integration](https://mlsanity.com/paper/2409.13724/) (2024)
- [Enhancing Reasoning Capabilities of LLMs via Principled Synthetic Logic Corpus](https://mlsanity.com/paper/2411.12498/) (2024)
- [A Systematic Comparison of Syllogistic Reasoning in Humans and Language Models](https://mlsanity.com/paper/2311.00445/) (2023)
- [Step-by-Step Fact Verification System for Medical Claims with Explainable Reasoning](https://mlsanity.com/paper/2502.14765/) (2025)
- [Unmasking Digital Falsehoods: A Comparative Analysis of LLM-Based Misinformation Detection Strategies](https://mlsanity.com/paper/2503.00724/) (2025)
- [Do Large Language Models Understand Conversational Implicature -- A case study with a chinese sitcom](https://mlsanity.com/paper/2404.19509/) (2024)
- [Shifting Perspectives: Steering Vectors for Robust Bias Mitigation in LLMs](https://mlsanity.com/paper/2503.05371/) (2025)
- [Comparing Inferential Strategies of Humans and Large Language Models in Deductive Reasoning](https://mlsanity.com/paper/2402.14856/) (2024)
- [The Missing Parts: Augmenting Fact Verification with Half-Truth Detection](https://mlsanity.com/paper/2508.00489/) (2025)
- [Enhancing Logical Reasoning in Language Models via Symbolically-Guided Monte Carlo Process Supervision](https://mlsanity.com/paper/2505.20415/) (2025)

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

- [SoK: Formal Methods for Fact-Checking and Information Integrity](https://mlsanity.com/paper/2609.23239/) (2026)

## Abstract (arXiv)

As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some neurosymbolic systems verify claims by using LLMs to translate natural language into logical formulae and then checking whether the proposed claims are logically sound, i.e. whether they can be validly derived from premises that are verified to be true. We argue that such approaches structurally fail to detect misleading claims due to systematic divergences between conclusions that are logically sound and inferences that humans typically make and accept. Drawing on studies in cognitive science and pragmatics, we present a typology of cases in which logically sound conclusions systematically elicit human inferences that are unsupported by the underlying premises. Consequently, we advocate for a complementary approach: leveraging human-like reasoning tendencies of LLMs as a feature rather than a bug, and using these models to validate the outputs of formal components in neurosymbolic systems against potentially misleading conclusions.