This paper introduces a logic to reason about a well-known model of opinion dynamics in socialnetworks initially developed by Morris DeGroot as well as Keith Lehrer and Carl Wagner. The proposed logic is an extension of Lukasiewicz' famous fuzzy logic with additional equational expressivity, modal operators, machinery from hybrid logic, and dynamic modalities. The model of opinion dynamics in social networks is simple enough to be easily grasped, but still complex enough to have interesting mathematical properties and applications. Thus, developing (...) a logic to reason about this particular model serves as a paradigmatic example of how logic can be useful in social network analysis. (shrink)

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. (shrink)

This paper introduces a general logical framework for reasoning about diffusion processes within social networks. The new “Logic for Diffusion in Social Networks” is a dynamic extension of standard hybrid logic, allowing to model complex phenomena involving several properties of agents. We provide a complete axiomatization and a terminating and complete tableau system for this logic and show how to apply the framework to diffusion phenomena documented in social networks analysis.

In this paper1, we develop an epistemic logic to specify and reason about the information flow on the underlying communication channels. By combining ideas from Dynamic Epistemic Logic (DEL) and Interpreted Systems (IS), our semantics offers a natural and neat way of modelling multi-agent communication scenarios with different assumptions about the observational power of agents. We relate our logic to the standard DEL and IS..

In this paper, we investigate the social herding phenomenon known as informational cascades, in which sequential inter-agent communication might lead to epistemic failures at group level, despite availability of information that should be sufficient to track the truth. We model an example of a cascade, and check the correctness of the individual reasoning of each agent involved, using two alternative logical settings: an existing probabilistic dynamic epistemic logic, and our own novel logic for counting evidence. Based on this analysis, we (...) conclude that cascades are not only likely to occur but are sometimes unavoidable by "rational" means: in some situations, the group’s inability to track the truth is the direct consequence of each agent’s rational attempt at individual truth-tracking. Moreover, our analysis shows that this is even so when rationality includes unbounded higher-order reasoning powers, as well as when it includes simpler, non-Bayesian forms of heuristic reasoning. (shrink)

The logic of acceptance and rejection (AEL2) is a nonmonotonic formalism to represent states of knowledge of an introspective agent making decisions about available information. Though having much in common, AEL2 differs from Moore's autoepistemic logic (AEL) by the fact that the agent not only can accept or reject a given fact, but he/she also has the possibility not to make any decision in case he/she does not have enough knowledge.