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In this work we have studied a very simple class of opinion diffusion processes on networks, which we called Boolean DeGroot processes (BDPs). Interestingly these processes lie at the interface of two so far unconnected network diffusion models: the well-known DeGroot processes---of which BDPs constitute the binary special case---and of propositional opinion diffusion processes---of which BDPs constitute the special case where the set of neighbors is a singleton. We established necessary and sufficient conditions for convergence for such processes and showed how these can be captured in modal fixpoint logics. These results have also provided a novel perspective on the issue of delegation cycles in liquid democracy.  In this work we have applied BDPs to a multiple-referenda set up, modeled in a binary aggregation framework. Our goal is now to integrate such processes in a fully-fledged judgment aggregation setting \cite{Grossi_2014} studying opinion diffusion in the presence of interdependences between the issues, that is introducing constraints into the binary aggregation framework. This a question that no existing work has addressed so far (cf. \cite\cite{Grandi:2015:POD:2772879.2773278}) and  will give rise to a variety of different dynamics depending on how issue-inconsistencies are treated by individuals. \paragraph{Acknowledgments} Both Zo\'{e} Christoff and Davide Grossi acknowledge support for this research by EPSRC (grant EP/M015815/1, ``Foundations of Opinion Formation in Autonomous Systems'').