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

Abstract

 Large Language Models (LLMs) are predominantly governed by probabilistic frameworks 
in which the sum of outcome probabilities is constrained to unity. This limitation, often imposed by 
Softmax layers, leads to a collapse of uncertainty that conflates ignorance, paradox, and vagueness. 
We present an empirical investigation of Neutrosophic Logic, in which Truth (T), Indeterminacy (I), 
and Falsity (F) are three independent dimensions on [0, 1], applied to elicit declared epistemic states 
from LLMs. Across 300 API calls — including 100 valid unconstrained neutrosophic evaluations — 
on four OpenAI GPT models and five linguistic phenomena (five repetitions per cell), the 
neutrosophic strategy yields hyper-truth (T + I + F > 1) in 66.0% of Strategy-1 evaluations, with the 
highest rates observed in ethical contradiction (95%) and future contingency (70%). A Pearson chi
square test of phenomenon × hyper-truth association is significant (chi-square = 11.32, df = 4, p = 
0.023). Mason (2026) independently replicated and extended an earlier release of this work across 
five additional model families from five different vendors, reporting hyper-truth in 84% of 
unconstrained evaluations. We do not claim that hyper-truth is an intrinsic latent variable inside the 
model; rather, that unconstrained neutrosophic prompting elicits declared epistemic states that 
probabilistic prompting structurally suppresses by Proposition 1. 

DOI 10.5281/zenodo.19954582