A categorical formalization of epistemic uncertainty frameworks

TL;DR

This paper introduces a categorical framework for epistemic uncertainty, unifying various theories like possibility and Bayesian updating through enriched category theory, providing a formal foundation for studying and transforming epistemic models.

Contribution

It develops a general categorical formalization of epistemic calculi, enabling systematic comparison, transformation, and unification of different uncertainty frameworks.

Findings

Unified categorical framework for epistemic uncertainty theories

Derived Bayesian updating and possibilistic conditioning as special cases

Provided tools for transforming and relating different epistemic models

Abstract

Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired by work of Opdan, we introduce a general category theoretic definition of epistemic calculi, which we use as a foundation for modelling and studying contradictions and synergies between several philosophical epistemological concepts. We further develop an enriched category theoretic process for changing calculi, and use this to study relationships between existing examples, like possibility theory and certainty factors. Finally, we introduce a general categorical form of belief updating based on change of enrichment, and prove that Bayesian updating and possibilistic conditioning arise as examples.