Human and AI-generated texts between modal logic and statistics

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 mathsfB, mathsf4, mathsf5, mathsfD. Each degree is at once the proportion of instances of a rule that the subframe licenses in Negri's labelled calculus mathsfG3.K and a plug-in estimate of a population probability. A prompt-balanced comparison finds consistently higher artificial degrees for mathsf4 and mathsf5. 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.