Classical Explanations in (and of) General Probabilistic Theories

2026-03-05

AI Summary

This work investigates how to formalize the notion of one probabilistic model “explaining” another within the framework of generalized probabilistic theories. The authors introduce a concept of explanation based on a specific span structure in the category of probability (Prob) and employ pullback constructions to compose such explanations. Their main contribution is a proof that every locally finite probabilistic model admits a canonical, sharp classical explanation. Furthermore, they establish a canonical functorial mapping from locally finite probabilistic theories to classical—typically nonlocal—theories, thereby demonstrating that generalized probabilistic models are classically interpretable in a precise, structured sense.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• probabilistic models
• classical explanation
• general probabilistic theories
• category theory
• local finiteness

Innovation

• probabilistic models
• category theory
• classical explanation
• pullback composition
• functorial representation