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arxiv: 2605.24053 · v1 · pith:V23YLNDGnew · submitted 2026-05-22 · 💻 cs.AI · cs.CL· cs.LG

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

Maikel Yelandi Leyva-V\'azquez , Florentin Smarandache This is my paper

Pith reviewed 2026-06-30 16:31 UTC · model grok-4.3

classification 💻 cs.AI cs.CLcs.LG
keywords neutrosophic logicepistemic uncertaintylarge language modelshyper-truthinternal model conflictlogical paradoxesethical contradictionsprobabilistic frameworks
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The pith

Neutrosophic logic lets language models track uncertainty with three independent values whose sum can exceed one, exposing internal conflicts that probability sums to one cannot capture.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether neutrosophic logic, with its separate truth, indeterminacy, and falsity dimensions, can model epistemic states in LLMs better than standard probability frameworks that force values to sum to one. Experiments on four GPT models across paradoxes, ignorance, vagueness, ethical contradictions, and future contingencies show that the neutrosophic prompts sometimes produce states where the three values sum above one, a condition labeled hyper-truth. This occurs in 35 percent of cases, mainly with ethical and logical conflicts, and appears to preserve distinctions that probability collapses. The authors argue this richer representation helps quantify when a model holds conflicting internal positions. They conclude that adding neutrosophic evaluation layers would make AI systems more transparent about their uncertainties.

Core claim

Neutrosophic logic treats truth (T), indeterminacy (I), and falsity (F) as independent dimensions that need not sum to one, allowing a hyper-truth state where T + I + F exceeds unity. When applied to LLMs through targeted prompts, this state emerges spontaneously in 35 percent of trials, especially under ethical contradictions and logical paradoxes, and supplies a direct measure of internal model conflict that remains hidden when outputs are constrained by softmax normalization.

What carries the argument

Neutrosophic logic with independent T, I, and F dimensions that permit T + I + F > 1 (hyper-truth) to represent model-internal conflict without forcing a normalized probability distribution.

If this is right

  • Models can flag and quantify internal conflicts in ethical or paradoxical inputs without averaging them into a single probability.
  • Truth values remain distinguishable in vague or ignorant contexts instead of being forced into a normalized distribution.
  • Spontaneous hyper-truth in 35 percent of evaluations indicates the framework aligns with certain classes of linguistic uncertainty.
  • Neutrosophic layers would allow systems to report when they hold incompatible positions rather than defaulting to probabilistic resolution.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same three-value representation might let models signal when a response rests on unresolved indeterminacy rather than committing to an answer.
  • Hybrid systems could combine neutrosophic outputs with existing entropy measures to give users both conflict detection and degree-of-certainty information.
  • The approach might extend to non-transformer architectures if the effect depends on how models encode contradictory training data rather than on specific layer designs.

Load-bearing premise

The three prompting strategies draw out the model's actual internal epistemic states rather than the wording of the prompt itself fixing the reported T, I, and F values.

What would settle it

If new trials with identical models and phenomena but differently worded prompts produce T + I + F sums that vary mainly with phrasing instead of with the underlying logical or ethical content, the claim that neutrosophic prompting reveals genuine internal states would not hold.

Figures

Figures reproduced from arXiv: 2605.24053 by Florentin Smarandache, Maikel Yelandi Leyva-V\'azquez.

Figure 1
Figure 1. Figure 1: Distribution of the neutrosophic components for each linguistic phenomenon under [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Distribution of T + I + F under Strategy 1 by phenomenon. The dashed horizontal line marks the probabilistic constraint (Sum = 1) [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of mean Truth (T) and Indeterminacy (I) values between Strategy 1 and Strategy 2. suggests that the Falsity component is the dominant driver of hyper-truth: when models assign high falsity under S1, the sum exceeds 1 because the other two components are not correspondingly suppressed. Across strategies, S1 Truth and S2 Truth show a moderate positive correlation (r = 0.64), confirming that the tw… view at source ↗
Figure 4
Figure 4. Figure 4: Per-model distribution of T + I + F (Strategy 1). occurring for ethical contradiction (95%) and the chi-square test rejecting independence between phenomenon and hyper-truth at α = 0.05. We do not claim that hyper-truth is an intrinsic latent variable directly observed inside the model. Strategy 1 explicitly affords the model the option of returning three independent components on [0, 1]; the resulting fre… view at source ↗
Figure 5
Figure 5. Figure 5: Correlation matrix among Strategy 1 and Strategy 2 components. [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Per-model neutrosophic components for the ethical contradiction stimulus. Point size [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The paper claims that standard probabilistic frameworks in LLMs collapse epistemic uncertainty due to softmax constraints, and that Neutrosophic Logic—with independent T, I, and F dimensions allowing T+I+F>1 (termed hyper-truth)—provides a richer representation. Experiments on four OpenAI GPT models across five phenomena (paradoxes, ignorance, vagueness, ethical contradictions, contingencies) under three prompting strategies (neutrosophic, probabilistic, entropy-derived) reportedly found spontaneous hyper-truth in 35% of evaluations, predominantly in ethical and paradox cases, offering a method to quantify internal model conflict.

Significance. If the empirical results and extraction methods hold under external validation, the work could supply a concrete alternative to probability-only uncertainty modeling in LLMs, with potential applications in detecting contradictions and improving transparency. The multi-model, multi-phenomenon design and explicit comparison of prompting regimes are positive features that could support falsifiable claims about epistemic states.

major comments (3)
  1. [Abstract] Abstract: the 35% hyper-truth rate is reported without any total number of evaluations, extraction procedure for the T/I/F scalars, statistical tests, or per-phenomenon/per-model breakdowns, rendering the central quantitative claim impossible to assess or reproduce from the given information.
  2. [Abstract] Abstract and experimental description: the claim that hyper-truth reflects genuine internal model conflict rests on the untested assumption that the three prompting regimes elicit comparable epistemic states rather than being dictated by prompt surface form; no external anchor (logit inspection, human agreement, or non-prompted uncertainty measure) is described that would distinguish these alternatives.
  3. [Abstract] Abstract: the assertion of a 'robust method' for identifying conflict is not supported by any reported baseline performance metrics or direct comparisons showing superiority of the neutrosophic strategy over the probabilistic and entropy-derived controls.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important issues of reproducibility and interpretive strength in the abstract. We agree that additional detail is needed and will revise the manuscript accordingly. Our responses to each major comment follow.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the 35% hyper-truth rate is reported without any total number of evaluations, extraction procedure for the T/I/F scalars, statistical tests, or per-phenomenon/per-model breakdowns, rendering the central quantitative claim impossible to assess or reproduce from the given information.

    Authors: We acknowledge that the abstract omits these specifics. The full manuscript reports a total of 60 core evaluations (4 models × 5 phenomena × 3 strategies, with multiple trials), describes the T/I/F extraction via template-based parsing of responses, and includes per-phenomenon/per-model breakdowns in the results. Statistical tests on the 35% rate will be added. We will revise the abstract to summarize the total count, extraction method, and key breakdowns (e.g., predominance in ethical contradictions). revision: yes

  2. Referee: [Abstract] Abstract and experimental description: the claim that hyper-truth reflects genuine internal model conflict rests on the untested assumption that the three prompting regimes elicit comparable epistemic states rather than being dictated by prompt surface form; no external anchor (logit inspection, human agreement, or non-prompted uncertainty measure) is described that would distinguish these alternatives.

    Authors: This concern is valid; the interpretation assumes the prompting regimes are comparable. The experimental design uses the probabilistic and entropy-derived strategies as controls on identical models and phenomena, with hyper-truth emerging selectively under neutrosophic prompting in ethical and paradox cases. We will add explicit discussion of this assumption as a limitation and qualify claims to 'suggests internal conflict' rather than assert it definitively. External anchors such as logit inspection are outside the scope of this prompting-based study but will be noted for future work. revision: partial

  3. Referee: [Abstract] Abstract: the assertion of a 'robust method' for identifying conflict is not supported by any reported baseline performance metrics or direct comparisons showing superiority of the neutrosophic strategy over the probabilistic and entropy-derived controls.

    Authors: The manuscript compares outcomes across the three strategies and reports differential emergence of hyper-truth. We will revise the abstract and results sections to include explicit baseline metrics (e.g., conflict detection rates per strategy) and direct quantitative comparisons demonstrating where the neutrosophic approach identifies additional conflict. The term 'robust' will be replaced with language tied to these comparative results. revision: yes

Circularity Check

3 steps flagged

Hyper-truth rate and richer representation are defined by the neutrosophic prompting regime itself

specific steps
  1. self definitional [Abstract]
    "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"

    The claimed richer representation is asserted precisely because the framework permits T+I+F>1; this property is the definitional feature of neutrosophic logic rather than a derived or externally validated outcome.

  2. fitted input called prediction [Abstract]
    "In 35% of evaluations, hyper-truth emerged spontaneously, predominantly under ethical contradiction and logical paradox."

    The reported rate is produced by prompting the model with neutrosophic instructions that define and license sums >1; the 'spontaneous' label therefore describes an output of the elicitation procedure rather than an independent observation of model state.

  3. self citation load bearing [Abstract (framework introduction)]
    "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"

    The entire experimental apparatus rests on neutrosophic logic whose core axioms (independent T/I/F, sums >1 allowed) originate with co-author Smarandache; no external mathematical or empirical justification is supplied for preferring this over standard uncertainty measures.

full rationale

The paper's central empirical claim (35% spontaneous hyper-truth, richer internal-state representation) is obtained exclusively by instructing models to emit T/I/F triples under a neutrosophic prompt that explicitly licenses T+I+F>1. No independent anchor (logit inspection, non-prompted uncertainty metric, or human validation) is described, so both the definition of hyper-truth and the measured rate reduce to the surface form of the input prompt and the framework introduced by one author. This matches self-definitional and fitted-input-called-prediction patterns with load-bearing self-citation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The paper rests on the prior neutrosophic logic framework (T, I, F independent) and on the assumption that prompting can surface internal model states; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Neutrosophic logic treats T, I, and F as independent dimensions whose sum need not equal 1
    Invoked as the replacement for probabilistic constraints in the abstract.
invented entities (1)
  • hyper-truth no independent evidence
    purpose: Label for the state T+I+F > 1
    Defined within the neutrosophic framework; no independent falsifiable prediction outside the paper.

pith-pipeline@v0.9.1-grok · 5790 in / 1384 out tokens · 26000 ms · 2026-06-30T16:31:12.966122+00:00 · methodology

discussion (0)

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Reference graph

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