人类与AI生成文本：模态逻辑与统计学之间
Human and AI-generated texts between modal logic and statistics
- University of Calabria（卡拉布里亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过将语义邻域图视为模态逻辑框架，利用统计验证程度区分人类与AI生成文本，发现AI在传递性和欧几里得性公理上程度更高。
AI中文摘要：
我们将语义邻域图的几何结构解读为模态逻辑，并赋予该解读一种统计形式，以精确刻画人类与机器生成文本之间的结构差异。文本被视为一个有限框架中的世界，其可达关系由Transformer嵌入的$k$-最近邻关系定义。我们展示了两个子语料库在对称性、传递性、欧几里得性和序列性上的频率，作为模态公理$\mathsf{B}$、$\mathsf{4}$、$\mathsf{5}$、$\mathsf{D}$的验证程度。每个程度既是子框架在Negri的带标签演算$\mathsf{G3.K}$中所许可的规则实例的比例，也是总体概率的插件估计。一项提示平衡的比较发现，对于$\mathsf{4}$和$\mathsf{5}$，人工生成的文本始终具有更高的程度。我们还增加了接地性和情境性的程度，并将许可解读重新表述为Cuconato的单边序贯风格tableaux，其中每个程度变为集合成员资格的比率。
英文摘要：
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.
