Human and AI-generated texts between modal logic and statistics

arXiv:2609.20311v1 Announce Type: cross 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.

Source: arXiv cs.AI | 2026-09-18