Traditional Business Process Management (BPM) focuses on discrete events and fails to incorporate critical continuous sensor data in cyber-physical environments. Hybrid declarative specifications, using Signal Temporal Logic (STL), address this limitation by allowing constraints over both discrete events and real-valued signals. However, existing work has been limited to monitoring and post-hoc conformance checking. This paper introduces a novel execution architecture based on Complex Event Processing (CEP) that enables the real-time execution and enforcement of hybrid declarative models. Our three-layer approach integrates STL-inspired predicates into the execution flow, allowing the system to actively trigger activities and enforce process boundaries based on continuous sensor behavior. This approach bridges the gap between hybrid specification and operational control.