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Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks


We take a logical approach to threshold models, used to study the diffusion of opinions, new technologies, infections, or behaviors in social networks. Threshold models consist of a network graph of agents connected by a social relationship and a threshold value which regulates the diffusion process. Agents adopt a new behavior/product/opinion when the proportion of their neighbors who have already adopted it meets the threshold. Under this diffusion policy, threshold models develop dynamically towards 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’ behavior allows agents to anticipate changes in behavior of their closer neighbors. Overall, our logical formalism captures the interplay between the epistemic and social dimensions in social networks.


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We would like to thank the anonymous reviewers for their insightful comments. Zoé Christoff acknowledges support for this research by the Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/M015815/1 “Foundations of Opinion Formation in Autonomous Systems”, as well as from the Deutsche Forschungsgemeinschaft (DFG) and Grantová agentura České republiky (GAČR) joint project RO 4548/6–1 “From Shared Evidence to Group Attitudes”. The contribution of Rasmus K. Rendsvig to the research reported in this article was funded by the Swedish Research Council through the framework project ‘Knowledge in a Digital World’ (Erik J. Olsson, PI). The Center for Information and Bubble Studies is sponsored by the Carlsberg Foundation.

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Correspondence to Rasmus K. Rendsvig.

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Edited by Giacomo Bonanno, Wiebe Van Der Hoek and Andres Perea

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Baltag, A., Christoff, Z., Rendsvig, R.K. et al. Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks. Stud Logica 107, 489–531 (2019).

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  • Social network theory
  • Threshold models
  • Diffusion in networks
  • Social epistemology
  • Formal epistemology
  • Dynamic epistemic logic
  • Opinion dynamics
  • Opinion dynamics under uncertainty