Convergence, Continuity and Recurrence in Dynamic Epistemic Logic

TL;DR

This paper introduces a topological framework for dynamic epistemic logic, linking discrete logical updates with continuous dynamical systems, and investigates convergence and recurrence properties within this setting.

Contribution

It develops a topological approach to dynamic epistemic logic, establishing conditions for logical convergence and recurrence using Stone topology and continuous mappings.

Findings

Logical convergence is equivalent to Stone topology convergence.

Action model transformations are continuous in the Stone topology.

Recurrent behavior of the induced maps is characterized.

Abstract

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps.