Studia Logica

, Volume 107, Issue 3, pp 489–531 | Cite as

Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks

  • Alexandru Baltag
  • Zoé Christoff
  • Rasmus K. RendsvigEmail author
  • Sonja Smets
Open Access


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.


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



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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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of PhilosophyUniversity of BayreuthBayreuthGermany
  3. 3.Center for Information and Bubble StudiesUniversity of CopenhagenCopenhagenDenmark

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