{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20311",
  "author_total": 2,
  "authors": [
    {
      "name": "Simone Cuconato"
    },
    {
      "name": "Donato Ferrari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a2x1j7h49p136.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20311",
  "fulltext_url": null,
  "id": "a2x1j7h49p136",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20311",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.AI"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Logic, Reasoning, and Knowledge"
    ]
  ],
  "openalex": "W7213612654",
  "pdf_url": "https://arxiv.org/pdf/2609.20311",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a2x1j7h49p136.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20311",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20311"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Human and AI-generated texts between modal logic and statistics",
  "title_text": "Human and AI-generated texts between modal logic and statistics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:29Z",
  "url": "https://research.draconitic.com/paper/a2x1j7h49p136",
  "venue": "arXiv",
  "versions": []
}