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)

In a recent paper, Christian List has argued for the compatibilism of free will and determinism. Drawing on a distinction between physical possibility and agential possibility, List constructs a formal two-level model in which the two concepts are consistent. This paper's first contribution is to show that though List's model is formally consistent, philosophically it falls short of establishing a satisfactory compatibilist position. Ensuingly, an analysis of the shortcomings of the model leads to the identification of a controversial epistemological assumption (...) implicit in the statements of both compatibilist and incompatibilist positions. Arguing that this assumption is not currently satisfied, the paper's second contribution is to show that neither the compatibilist nor the incompatibilist position is presently well-founded. (shrink)

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action (...) model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps. (shrink)

It has become a truism that we live in so-called information societies where new information technologies have made information abundant. At the same time, information science has made us aware of many phenomena tied to the way we process information. This article explores a series of socio-epistemic information phenomena resulting from processes that track truth imperfectly: pluralistic ignorance, informational cascades, and belief polarization. It then couples these phenomena with the hypothesis that modern information technologies may lead to their amplification so (...) as to give rise to what are called “infostorms.” This points to the need for studying further the exact relations between information technologies and such infostorms, as well as the ways we may design technologies to avoid being misled away from what we have good reasons to believe. (shrink)

In dynamical multi-agent systems, agents are controlled by protocols. In choosing a class of formal protocols, an implicit choice is made concerning the types of agents, actions and dynamics representable. This paper investigates one such choice: An intensional protocol class for agent control in dynamic epistemic logic, called ‘DEL dynamical systems’. After illustrating how such protocols may be used in formalizing and analyzing information dynamics, the types of epistemic temporal models that they may generate are characterized. This facilitates a formal (...) comparison with the only other formal protocol framework in dynamic epistemic logic, namely the extensional ‘DEL protocols’. The paper concludes with a conceptual comparison, highlighting modeling tasks where DEL dynamical systems are natural. (shrink)

The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept of logical (...) convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems. (shrink)

When information grows abundant, attention becomes a scarce resource. As a result, agents must plan wisely how to allocate their attention in order to achieve epistemic efficiency. Here, we present a framework for multi-agent epistemic planning with attention, based on Dynamic Epistemic Logic. We identify the framework as a fragment of standard DEL, and consider its plan existence problem. While it is undecidable in the general case, we show that when attention is required for learning, all instances of the problem (...) are decidable. (shrink)