Probabilistic Epistemic Updates on Algebras

TL;DR

This paper develops a duality-theoretic framework for probabilistic epistemic updates, providing algebraic characterizations and axiomatizations for intuitionistic probabilistic dynamic epistemic logic.

Contribution

It introduces a duality-based algebraic approach to probabilistic epistemic updates and axiomatizes the intuitionistic version of PDEL with soundness and completeness.

Findings

Duality characterization of product updates in PDEL models

Algebraic interpretation of PDEL language on Heyting algebras

Soundness and completeness of the axiomatization for intuitionistic PDEL

Abstract

The present paper contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. Thanks to this construction, an interpretation of the language of PDEL can be defined on algebraic models based on Heyting algebras. This justifies our proposal for the axiomatization of the intuitionistic counterpart of PDEL, of which prove soundness and completeness with respect to algebraic probabilistic epistemic models.