Classical Explanations in (and of) General Probabilistic Theories

TL;DR

This paper introduces a formal notion of explanation between probabilistic models within a categorical framework, demonstrating that every locally-finite model admits a canonical classical explanation and representation.

Contribution

It defines a new categorical concept of explanation for probabilistic models and shows the existence of canonical classical explanations for locally-finite models.

Findings

Explanations compose via a pullback construction.

Every locally-finite probabilistic model has a canonical, sharp classical explanation.

The construction is functorial, providing a canonical classical representation.

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.