Dynamic Logics for Threshold Models and their Epistemic Extension
(2014) ELISIEM - Epistemic Logic for Individual, Social, and Interactive Epistemology : Workshop at the 26th European Summer School in Logic, Language and Information- 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:
https://lup.lub.lu.se/record/5155054
- author
- Christoff, Zoé and Rendsvig, Rasmus Kraemmer LU
- organization
- publishing date
- 2014
- type
- Contribution to conference
- publication status
- unpublished
- subject
- keywords
- Epistemic Logic, Prediction, Social Networks, Logic, Social Influence, Rationality, Threshold Model
- conference name
- ELISIEM - Epistemic Logic for Individual, Social, and Interactive Epistemology : Workshop at the 26th European Summer School in Logic, Language and Information
- conference location
- Tübingen, Germany
- conference dates
- 2014-08-11 - 2014-08-15
- 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}},
keywords = {{Epistemic Logic; Prediction; Social Networks; Logic; Social Influence; Rationality; Threshold Model}},
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}},
}