Classical Explanations in (and of) General Probabilistic Theories

John Harding; Alex Wilce

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arXiv · 2603.05627

Classical Explanations in (and of) General Probabilistic Theories

John Harding·Alex Wilce

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Abstract

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.

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John Harding, Alex Wilce. 2026-03-05. Classical Explanations in (and of) General Probabilistic Theories. https://arxiv.org/abs/2603.05627

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