Convergence, Continuity and Recurrence in Dynamic Epistemic Logic
This work addresses a foundational problem in logic and dynamical systems theory, but it appears incremental as it builds on existing topological methods.
The paper tackles the problem of analyzing dynamic epistemic logic from a topological perspective, resulting in a framework that satisfies the requirements for a topological dynamical system, with maps induced by action model transformations shown to be continuous and results on recurrent behavior presented.
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.