  This paper focuses on the convergence of infor- mation in distributed systems
of agents communicating over a network. The information on which the
convergence is sought is not represented by real numbers, rather by sets of
real numbers, whose possible dynamics are given by the class of so-called
Boolean maps, involving only unions, intersections, and complements of sets.
Based on a notion of contractivity, a necessary and sufficient condition
ensuring the global and local convergence toward an equilibrium point is
presented. In particular the analysis of global convergence recovers results
already obtained by the authors, but the more general approach used in this
paper allows analogue results to be found to characterize the local
convergence.
