Convergence, Continuity and Recurrence in Dynamic Epistemic Logic
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.
Cite
@article{arxiv.1709.00359,
title = {Convergence, Continuity and Recurrence in Dynamic Epistemic Logic},
author = {Dominik Klein and Rasmus K. Rendsvig},
journal= {arXiv preprint arXiv:1709.00359},
year = {2017}
}
Comments
As appearing in "Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan)", LNCS, Springer 2017