We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard pullback construction (notwithstanding that $\Prob$ does not support arbitrary pullbacks). We then show that every locally-finite probabilistic model has a canonical, sharp classical explanation. The construction is functorial, so every locally-finite probabilistic theory has a canonical, sharp classical (though of course, usually non-local) representation.

翻译：我们引入了一种概念，即通过另一种（广义）概率模型对一种概率模型的“解释”，作为概率模型与态射构成的范畴$\Prob$中的一种特定跨度。我们证明了在标准拉回构造下（尽管$\Prob$不支持任意拉回），解释具有复合性。随后，我们证明每个局部有限概率模型都存在一个典范的、锐利的经典解释。该构造具有函子性，因此每个局部有限概率理论都拥有一个典范的、锐利的经典（尽管通常是非定域性的）表示。