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arXiv · 2609.20311

Human and AI-generated texts between modal logic and statistics

Simone Cuconato·Donato Ferrari
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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 $\mathsf{B}$, $\mathsf{4}$, $\mathsf{5}$, $\mathsf{D}$. Each degree is at once the proportion of instances of a rule that the subframe licenses in Negri's labelled calculus $\mathsf{G3.K}$ and a plug-in estimate of a population probability. A prompt-balanced comparison finds consistently higher artificial degrees for $\mathsf{4}$ and $\mathsf{5}$. 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.

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BibTeXRIS

Simone Cuconato, Donato Ferrari. 2026-07-31. Human and AI-generated texts between modal logic and statistics. https://arxiv.org/abs/2609.20311

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