  In this paper we introduce a novel consensus mech- anism where agents of a
network are able to share logical values, or Booleans, representing their local
opinions on e.g. the presence of an intruder or of a fire within an indoor
environment. We first formulate the logical consensus problem, and then we
review relevant results in the literature on cellular automata and convergence
of finite-state iteration maps. Under suitable joint conditions on the
visibility of agents and their communication capability, we provide an
algorithm for generating a logical linear consensus system that is globally
stable. The solution is optimal in terms of the number of messages to be
exchanged and the time needed to reach a consensus. Moreover, to cope with
possible sensor failure, we propose a second design approach that produces
robust logical nonlinear consensus systems tolerating a given maximum number of
faults. Finally, we show applicability of the agreement mechanism to a case
study consisting of a distributed Intrusion Detection System (IDS).
