We consider cyber-physical systems (CPSs) comprising a central controller that might be replicated for high-reliability, and one or more process agents. The controller receives measurements from process agents, causing it to compute and issue setpoints that are sent back to process agents. The implementation of these setpoints causes a change in the state of the controlled physical process, and the new state is communicated to the controllers through resulting measurements. To ensure correct operation, the process agents must implement only those setpoints that were caused by their most recent measurements. However, in the presence of replication of the controller, network or computation delays, setpoints and measurements do not necessarily succeed in causing the intended behavior. To capture the dependencies among events associated with measurements and setpoints, we introduce the intentionality relation among such events in a CPS and illustrate its differences with respect to the happened-before relation. We propose a mechanism, intentionality clocks, and the design of controllers and process agents that can be used to guarantee the strong clock-consistency condition under the intentionality relation. Moreover, we prove that our design ensures correct operation despite crash, delay, and network faults. We also demonstrate the practical application of our abstraction through an illustration with a real-world CPS for electrical vehicles.