Human and AI-generated texts between modal logic and statistics
Abstract
We read the geometry of semantic neighbourhood graphs as modal logic and give that reading a statistical form, in order to make precise the structural difference between human and machine-generated text. Texts are the worlds of a finite frame whose accessibility is the k-nearest-neighbour relation of a transformer embedding, and the symmetry, transitivity, Euclideanity and seriality frequencies of the two subcorpora are shown to be degrees of validation of the modal axioms B, 4, 5, D. Each degree is at once the proportion of instances of a rule that the subframe licenses in Negri's labelled calculus G3.K and a plug-in estimate of a population probability. A prompt-balanced comparison finds consistently higher artificial degrees for 4 and 5. We add a degree of groundedness and of situatedness, and recast the licensing reading in Cuconato's one-sided sequent-style tableaux, where each degree becomes a rate of set membership.
Related
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BibTeX
@misc{cuconato2026human,
title = {{Human and AI-generated texts between modal logic and statistics}},
author = {Simone Cuconato and Donato Ferrari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20311},
eprint = {2609.20311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20311},
}
RIS
TY - UNPB
TI - Human and AI-generated texts between modal logic and statistics
AU - Simone Cuconato
AU - Donato Ferrari
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20311
UR - https://arxiv.org/abs/2609.20311
AB - We read the geometry of semantic neighbourhood graphs as modal logic and give that reading a statistical form, in order to make precise the structural difference between human and machine-generated text. Texts are the worlds of a finite frame whose accessibility is the k-nearest-neighbour relation of a transformer embedding, and the symmetry, transitivity, Euclideanity and seriality frequencies of the two subcorpora are shown to be degrees of validation of the modal axioms B, 4, 5, D. Each degree is at once the proportion of instances of a rule that the subframe licenses in Negri's labelled calculus G3.K and a plug-in estimate of a population probability. A prompt-balanced comparison finds consistently higher artificial degrees for 4 and 5. We add a degree of groundedness and of situatedness, and recast the licensing reading in Cuconato's one-sided sequent-style tableaux, where each degree becomes a rate of set membership.
ER -