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Convergence, Continuity and Recurrence in Dynamic Epistemic Logic

Klein, Dominik and Rendsvig, Rasmus K. LU (2017) Logic, Rationality, and Interaction In Logic, Rationality, and Interaction 10445 LNCS. p.108-122
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.

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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Convergence, Dynamic epistemic logic, Dynamical systems, General topology, Limit behavior, Metric spaces, Modal logic, Recurrence
in
Logic, Rationality, and Interaction
volume
10445 LNCS
pages
15 pages
publisher
Springer Verlag
conference name
Logic, Rationality, and Interaction
external identifiers
  • scopus:85029451739
ISSN
16113349
03029743
ISBN
9783319649993
DOI
10.1007/978-3-662-55665-8_8
language
English
LU publication?
yes
id
e966a224-bb29-4145-ba52-5a30d3a45934
date added to LUP
2017-10-05 07:38:58
date last changed
2018-02-20 15:37:18
@inbook{e966a224-bb29-4145-ba52-5a30d3a45934,
  abstract     = {<p>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.</p>},
  author       = {Klein, Dominik and Rendsvig, Rasmus K.},
  isbn         = {9783319649993},
  issn         = {16113349},
  keyword      = {Convergence,Dynamic epistemic logic,Dynamical systems,General topology,Limit behavior,Metric spaces,Modal logic,Recurrence},
  language     = {eng},
  pages        = {108--122},
  publisher    = {Springer Verlag},
  series       = {Logic, Rationality, and Interaction},
  title        = {Convergence, Continuity and Recurrence in Dynamic Epistemic Logic},
  url          = {http://dx.doi.org/10.1007/978-3-662-55665-8_8},
  volume       = {10445 LNCS},
  year         = {2017},
}