Abstract
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.
| Original language | English |
|---|---|
| Journal | Studia Logica: An International Journal for Symbolic Logic |
| Volume | 107 |
| Issue number | 3 |
| Pages (from-to) | 489-531 |
| Number of pages | 43 |
| ISSN | 0039-3215 |
| DOIs | |
| Publication status | Published - 15 Jun 2019 |
Keywords
- Faculty of Humanities
- Social network theory
- Threshold models
- Diffusion in networks
- Social epistemology
- Formal epistemology
- Dynamic epistemic logic
- Opinion dynamics
- Opinion dynamics under uncertainty