Convergence, Continuity and Recurrence in Dynamic Epistemic Logic

TY - GEN

T1 - Convergence, Continuity and Recurrence in Dynamic Epistemic Logic

AU - Klein, Dominik

AU - Rendsvig, Rasmus Kræmmer

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - https://arxiv.org/abs/1709.00359

U2 - 10.1007/978-3-662-55665-8_8

DO - 10.1007/978-3-662-55665-8_8

M3 - Article in proceedings

SN - 978-3-662-55664-1

T3 - Lecture notes in computer science

SP - 108

EP - 122

BT - Logic, Rationality and Interaction

A2 - Baltag, Alexandru

A2 - Seligman, Jeremy

A2 - Yamada, Tomoyuki

PB - Springer

CY - Berlin

ER -