We introduce a novel consensus mechanism by which the agents of a network can reach an agreement on the value of a shared logical vector function depending on binary input events. Based on results on the convergence of finite-state iteration systems, we provide a technique to design logical consensus systems that minimizing the number of messages to be exchanged and the number of steps before consensus is reached, and tolerating a bounded number of failed or malicious agents. We provide sufficient joint conditions on the input visibility and the communication topology for the method's applicability. We describe the application of our method to two distributed network intrusion detection problems. (C) 2013 Elsevier Ltd. All rights reserved.