We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences (...) of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect. (shrink)

This paper introduces a comprehensive logical framework to reason about threshold-driven diffusion and threshold-driven link change in social networks. It considers both monotonic dynamics, where agents can only adopt new features and create new connections, and non-monotonic dynamics, where agents may also abandon features or cut ties. Three types of operators are combined: one capturing diffusion only, one capturing link change only, and one capturing both at the same time. We first characterise the models on which diffusion of a unique (...) feature and link change stabilise, whilst discussing salient properties of stable models with multiple spreading features. Second, we show that our operators (and any combination of them) are irreplaceable, in the sense that the sequences of model updates expressed by a combination of operators cannot always be expressed using any other operators. Finally, we analyse classes of models on which some operators can be replaced. (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.