Industrial control systems monitor and control critical infrastructure assets such as the electric power grid, oil and gas pipelines, transportation systems and water treatment and supply facilities. Attacks that impact the operations of these critical assets could have devastating consequences to society. The complexity and interconnectivity of industrial control systems have introduced vulnerabilities and attack surfaces that previously did not exist. The numerous communications paths and ingress and egress points, technological diversity and strict operating requirements provide myriad opportunities for a motivated adversary. This paper investigates the detection of integrity errors in industrial control systems by correlating state values from field devices. Specifically, it considers a formulation of the classic Byzantine Generals Problem in the context of industrial control systems. The results demonstrate that leveraging physical system properties allows the inference of system states to identify integrity compromises.