In the era of Big Data and Internet-of-Things (IoT), all real-world environments are gradually becoming cyber-physical (e.g., emergency management, healthcare, smart manufacturing, etc.), with the presence of connected devices and embedded ICT systems (e.g., smartphones, sensors, actuators) producing huge amounts of data and events that influence the enactment of the Cyber Physical Processes (CPPs) enacted in such environments. A Process Management System (PMS) employed for executing CPPs is required to automatically adapt its running processes to anomalous situations and exogenous events by minimising any human intervention at run-time. In this paper, we tackle this issue by introducing an approach and an adaptive Cognitive PMS that combines process execution monitoring, unanticipated exception detection and automated resolution strategies leveraging on well-established action-based formalisms in Artificial Intelligence, which allow to interpret the ever-changing knowledge of cyber-physical environments and to adapt CPPs by preserving their base structure.