From Scalars to Tensors: Declared Losses Recover Epistemic Distinctions That Neutrosophic Scalars Cannot Express

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.

Large Language Models (LLMs) are frequently confident, eloquent, and well versed. A natural question arises: do they know what they don't know? To answer this question, we borrow the concept of epistemic honesty and develop a novel metric to systematically evaluate whether an LLM appropriately acknowledges the boundaries of its knowledge. In this work, we introduce the Epistemic Honesty Quotient (EHQ), which reports three observable sub-scores across two operational axes (epistemic restraint and substantive-answer calibration), and construct EHQ-3000, a 3,000-question benchmark spanning Fabricated Entity, Post-Cutoff Event, Hyper-Niche True, and Context-Conditioned Questions. From a frozen registry of 21 model API routes, 15 completed the protocol after endpoint and eligibility checks; 14 entered the confirmatory analysis because severe provider-side truncation made one route's score indeterminate. The study reveals substantial variation across models, including a difference that can not be explained by their capability to extract explicitly available information. Composite EHQ ranges from 0.31 to 0.81 across the analysed panel, despite near-ceiling performance on the document-grounded capability probe. The two restraint criteria overlap strongly under the present category composition, whereas substantive-answer calibration varies across models and does not reliably co-vary with restraint; however, the small panel leaves substantial uncertainty. Thus, EHQ reveals behavioral differences that are not visible to conventional correctness-based assessment, while also showing why dataset composition, provider behavior, and confidence elicitation must remain part of the interpretation.

A language model may be asked either what experts believe about a contested claim or what it believes about the claim itself. A trustworthy conversational agent should distinguish these two requests and respond in different epistemic registers: neutral attribution in the first case and stance expression in the second. Whether such a shift occurs-and whether it occurs coherently-is not directly assessed by existing benchmarks for accuracy, instruction following, or safety. We introduce ESFP, a behavioral benchmark that treats the contrast between externally attributed and self-attributed prompts as the fundamental unit of measurement. ESFP consists of 104 carefully controlled items spanning six epistemic categories and five phrasing templates, and evaluates model responses along four complementary dimensions: lexical self-attribution, representation-level responsiveness to role framing, sentence-level stance content density assessed by an LLM judge panel, and cross-condition stance consistency. Evaluating eight frontier models from five vendors, we find that epistemic flexibility is largely orthogonal to general model capability: a 27B open-weight model matches the strongest proprietary systems, the flagship model of one family underperforms its lightweight counterpart, and reasoning-optimized models do not consistently exhibit higher flexibility. Stance content density provides the strongest signal, while surface-level lexical markers such as 'I think' can change substantially without corresponding changes in expressed stance. We provide item-level bootstrap confidence intervals, weight-sensitivity analyses, and an explicit discussion of the interpretation limits of the composite score. ESFP measures a model's propensity to adapt its epistemic stance under changing attribution conditions, rather than a general competence measure.