Conflict or uncertainty? Reading the partial paraconsistency hierarchy of interval (T, I, N, U₁, …, Uₙ, F) tuples from language-model outputs

Florentin Smarandache; Maikel Leyva-Vázquez

doi:10.5281/zenodo.22954807

Authors

Florentin Smarandache University of New Mexico Author https://orcid.org/0000-0002-5560-5926 (unauthenticated)
Maikel Leyva-Vázquez Universidad Bernardo O’Higgins Author https://orcid.org/0000-0001-7911-5879 (unauthenticated)

DOI:

https://doi.org/10.5281/zenodo.22954807

Keywords:

paraconsistency, neutrosophic logic, multi-uncertainty, language models, elicitation, liar paradox

Abstract

Genuine conflict (truth and falsity both strongly supported) and plain uncertainty (weak support either way) are different epistemic situations, yet a single probability of truth reports both as the same kind of number. This feasibility study populates the partial paraconsistency hierarchy of interval (T, I, N, U₁, …, Uₙ, F) tuples from repeated outputs of gpt-4o-mini, deepseek-chat and the typed evaluation model Jev. All three systems declared the liar paradox Order-0, while intermediate orders were not read reliably. The study reports the elicitation protocol, a corrected scoring error, cross-model stability, limitations and requirements for a larger pre-registered study.