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\cite{Grossi_2014}  The paper focuses on a specific class of opinion diffusion processes in which opinions are binary, and agents copy the opinion of exactly one influencer, possibly themselves. Despite its simplicity, this model is of interest for two reasons. First, it corresponds to a class of processes which lies at the interface of two classes ofopinion  diffusion processes which have remained so far unrelated: the stochastic opinion diffusion model known as DeGroot's \cite{Degroot_1974}, and the more recent propositional opinion diffusion model due to \cite{Grandi:2015:POD:2772879.2773278}. The processes we study, called here Boolean DeGroot processes, are the $\set{0,1}$ limit case of the DeGroot stochastic processes and, at the same time, the limit case of propositional opinion diffusion processes where each agent has access to the opinion of exactly one neighbor.  Second, it provides an abstract model with which to analyze some aspects the popular, and currently much discussed, aggregation system called liquid democracy \cite{liquidfeedback}. \cite{liquid_feedback}. We will see that Boolean DeGroot processes offer a novel and natural angle on the issue of delegation cycles in liquid democracy.  \paragraph{Contributions of the paper}  The paper studies the convergence of Boolean DeGroot processes, characterizing them with necessary and sufficient conditions. In doing so the paper uses standard graph-theoretic tool as well as techniques from modal fixpoint logics, showing how those formalisms can play a useful role in studying qualitative models of opinion formation. The results we obtain on the characterization of convergence are then applied to provide novel insights into liquid democracy, which remains a rather underexplored system in the social-choice literature.  \paragraph{Outline of the paper}  Section \ref{sec:preliminaries} introduces the paper's notation and the key definition of Boolean DeGroot process. Section \ref{sec:convergence} studies necessary and sufficient conditions for those processes to converge. Section \ref{sec:logic} shows how off-the-shelf fixpoint logics (specifically the modal $\mu$-calculus) can be used to specifies properties of such processes formally. Section \ref{sec:liquid} shows how Boolean DeGroot processes relate to liquid democracy, contributing some novel insights into the understanding of delegation cycles. Section \ref{sec:conclusions} concludes the paper and sketches some on-going lines of research.