Categories for Dynamic Epistemic Logic

TL;DR

This paper reformulates the semantics of dynamic epistemic logic using category theory, providing a more natural and algebraic framework that facilitates model updates and integration with first-order logic.

Contribution

It introduces a categorical and algebraic reformulation of DEL semantics, highlighting the natural modeling of updates and enabling first-order DEL semantics.

Findings

Categorical perspective naturally captures model updates in DEL

Reformulation merges DEL with standard categorical semantics for first-order logic

Provides a more algebraic and structural understanding of DEL semantics

Abstract

The primary goal of this paper is to recast the semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and categories of Kripke frames, with particular emphasis on the duality between relations and adjoint homomorphisms. Using these categories, we then reformulate the semantics of DEL in a more categorical and algebraic form. Several virtues of the new formulation will be demonstrated: The DEL idea of updating a model into another is captured naturally by the categorical perspective -- which emphasizes a family of objects and structural relationships among them, as opposed to a single object and structure on it. Also, the categorical semantics of DEL can be merged straightforwardly with a standard categorical semantics for first-order logic, providing a semantics for first-order DEL.