Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks

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.

Dynamic Term-Modal Logic for Epistemic Social Network Dynamics

“…The existing work on epistemic network structures may be organized in terms of the static languages they work with: propositional modal logic [2,14] or hybrid logic [9-12, 18, 19, 21, 22]. In the former, the social network is described using designated atomic propositions (e.g., N ab for 'b is a neighbor of a').…”

“…Both de dicto and de re statements may partially be expressed in propositional languages (e.g. de dicto K a (p b ∨ p c ) vs. de re K a p b ∨ K a p c ; see [2] for such a usage), but not in a principled manner: the required formulas will depend on the specific circumstances. Fig.…”

“…We have been able to emulate the updates used in the examples of [22], but the general question is open. Further, the statics of frameworks that describe networks using propositional logic [2,14] must be DTML encodable, and we expect the name about their updates, where reduction axioms exist. This raises two questions: if we can show this by a general results instead of piecemeal, and whether principled DTML action models exist for classes of updates.…”

Reliability-based preference dynamics: lexicographic upgrade

“…Such approaches use qualitative tools instead of quantitative ones, and instead of looking at 'complex' data describing influence behaviour, they rely on relatively 'simple' models, using then formal languages to describe general 'complex' patterns about the system's behaviour. One of such proposals is the study of threshold model dynamics [60] from a logical perspective carried out in Baltag et al [10], which considers a set of agents, a behaviour p (or a set of them) that agents might or might not have, and a friendship relation among the agents themselves. In this setting, each agent will adopt behaviour p if and only if the proportion of her p-friends is at least the given threshold θ.…”

“…The proposal of this paper differs from threshold models in that what matters for an agent is not how many people has a given preference, but rather the preferences of certain people (namely, those she considers the most reliable ones). Still, Baltag et al [10] goes one step further, as it also incorporates an epistemic component, then making an agent's behaviour dependent not on other agents' behaviour, but rather on what she knows about other agents' behaviour.…”