# Breaking the Chains of Probability: Neutrosophic Logic as a New Framework for Epistemic Uncertainty in Large Language Models

arXiv: https://arxiv.org/abs/2605.24053 · HTML: https://mlsanity.com/paper/2605.24053/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Artificial Intelligence, Values and Alignment](https://mlsanity.com/paper/2001.09768/) (2020)
- [Better Zero-Shot Reasoning with Role-Play Prompting](https://mlsanity.com/paper/2308.07702/) (2023)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Mitigating LLM Hallucinations via Conformal Abstention](https://mlsanity.com/paper/2405.01563/) (2024)
- [Softmax is not Enough (for Sharp Size Generalisation)](https://mlsanity.com/paper/2410.01104/) (2024)
- [From Scalars to Tensors: Declared Losses Recover Epistemic Distinctions That Neutrosophic Scalars Cannot Express](https://mlsanity.com/paper/2604.09602/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are predominantly governed by probabilistic frameworks in which the sum of outcome probabilities is constrained to unity. This architectural limitation, often imposed by Softmax layers, leads to a collapse of uncertainty that makes it difficult to differentiate between epistemic uncertainty, paradox, and vagueness. We present an empirical investigation of the application of Neutrosophic Logic, a framework that treats Truth (T), Indeterminacy (I), and Falsity (F) as three independent dimensions, to model epistemic states in LLMs. We conducted experiments on a family of four OpenAI GPT models across five linguistic phenomena: logical paradoxes, epistemic ignorance, vagueness, ethical contradictions, and future contingencies, under three prompting strategies: neutrosophic, probabilistic, and entropy-derived. Our findings reveal that the neutrosophic approach, by allowing T+I+F > 1, a state we term hyper-truth, provides a richer representation of a model's internal state. In 35% of evaluations, hyper-truth emerged spontaneously, predominantly under ethical contradiction and logical paradox. We demonstrate that this approach preserves truth values in fuzzy contexts and offers a robust method for identifying and quantifying internal model conflict. We conclude that the integration of neutrosophic evaluation layers is a critical step toward more transparent, reliable, and ethically aware AI systems.