Concurrent and distributed systems are often prone to failures. Errors in modeling an agent’s behavior can propagate into large interacting systems with unexpected consequences. In this paper, we propose a theory for the process algebra CCS enriched with a formal and explicit representation of errors based on McCarthy’s style three-valued logic, which includes the traditional Boolean values and a third error value. In this setting, we formally study how the emergence of local errors may or may not result in propagation, as also emphasized in a real-world case study modeling a distributed microservices architecture.