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Dynamic Logics for Threshold Models and their Epistemic Extension

Christoff, Zoé and Rendsvig, Rasmus Kraemmer LU (2014)
Abstract
We take a logical approach to threshold models , used to study the diffusion of e.g. new technologies or behaviors in social net-works. In short, threshold models consist of a network graph of agents connected by a social relationship and a threshold to adopt a possibly cascading behavior. Agents adopt new behavior when the proportion of their neighbors who have already adopted it meets the threshold. Under this adoption policy, threshold models develop dynamically with a guaranteed fixed point. We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant... (More)
We take a logical approach to threshold models , used to study the diffusion of e.g. new technologies or behaviors in social net-works. In short, threshold models consist of a network graph of agents connected by a social relationship and a threshold to adopt a possibly cascading behavior. Agents adopt new behavior when the proportion of their neighbors who have already adopted it meets the threshold. Under this adoption policy, threshold models develop dynamically with a guaranteed fixed point. We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbors’ behaviors allows agents to anticipate changes in behavior of their closer neighbors. It is shown that this epistemic prediction dynamics is equivalent to the non-epistemic threshold model dynamics if and only if agents know exactly their neighbors’ behavior. We further show results regarding fixed points and convergence speed,and provide a partial set of reduction laws, venues for further research, and graphical representations of the dynamics. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to conference
publication status
unpublished
subject
keywords
Epistemic Logic, Prediction, Social Networks, Logic, Social Influence, Rationality, Threshold Model
project
Knowledge in a Digital World: Trust, Credibility and Relevance on the Web
language
English
LU publication?
yes
id
ee9cd532-fdac-4ac0-a5aa-80ee8c72f19f (old id 5155054)
alternative location
https://www.academia.edu/6864788/Dynamic_Logics_for_Threshold_Models_and_their_Epistemic_Extension_-_ELISIEM_2014
date added to LUP
2016-04-04 14:34:48
date last changed
2018-11-21 21:21:07
@misc{ee9cd532-fdac-4ac0-a5aa-80ee8c72f19f,
  abstract     = {We take a logical approach to threshold models , used to study the diffusion of e.g. new technologies or behaviors in social net-works. In short, threshold models consist of a network graph of agents connected by a social relationship and a threshold to adopt a possibly cascading behavior. Agents adopt new behavior when the proportion of their neighbors who have already adopted it meets the threshold. Under this adoption policy, threshold models develop dynamically with a guaranteed fixed point. We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbors’ behaviors allows agents to anticipate changes in behavior of their closer neighbors. It is shown that this epistemic prediction dynamics is equivalent to the non-epistemic threshold model dynamics if and only if agents know exactly their neighbors’ behavior. We further show results regarding fixed points and convergence speed,and provide a partial set of reduction laws, venues for further research, and graphical representations of the dynamics.},
  author       = {Christoff, Zoé and Rendsvig, Rasmus Kraemmer},
  language     = {eng},
  title        = {Dynamic Logics for Threshold Models and their Epistemic Extension},
  url          = {https://www.academia.edu/6864788/Dynamic_Logics_for_Threshold_Models_and_their_Epistemic_Extension_-_ELISIEM_2014},
  year         = {2014},
}