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Human and AI-generated texts between modal logic and statistics — arXiv:2609.20311

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.20311
License (as archived): CC0-1.0
Archived: 2026-10-10T03:24:14.141Z
SHA-256 of the archived text: 2490b40cc59addac6764e5dc5319a0b1be52b51ae83135aacd44da5ab62cf064
Stable URL of this page: https://metraipolis.com/documento/dc_032e6caec589

How to cite

Human and AI-generated texts between modal logic and statistics — arXiv:2609.20311 — arXiv (en), https://arxiv.org/abs/2609.20311 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_032e6caec589 (Metraipolis archive dc_032e6caec589, sha256 2490b40cc59addac6764e5dc5319a0b1be52b51ae83135aacd44da5ab62cf064)

BibTeX

@misc{dc032e6caec589,
  title = {Human and AI-generated texts between modal logic and statistics — arXiv:2609.20311},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.20311},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_032e6caec589; sha256 2490b40cc59addac6764e5dc5319a0b1be52b51ae83135aacd44da5ab62cf064},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.20311. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-18 in cs.AI).
Categorie arXiv: Logic (math.LO) ; Artificial Intelligence (cs.AI); Statistics Theory (math.ST).
Pagina del lavoro: https://arxiv.org/abs/2609.20311 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-10T03:04:13.942Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).