From biological systems to cyber-physical systems, monitoring the behavior of such dynamical systems often requires to reason about complex spatio-temporal properties of physical and/or computational entities that are dynamically interconnected and arranged in a particular spatial configuration. Spatio-Temporal Reach and Escape Logic (STREL) is a recent logic-based formal language designed to specify and to reason about spatio-temporal properties. STREL considers each systems entity as a node of a dynamic weighted graph representing their spatial arrangement. Each node generates a set of mixed-analog signals describing the evolution over time of computational and physical quantities characterising the nodes behavior. While there are offline algorithms available for monitoring STREL specifications over logged simulation traces, here we investigate for the first time an online algorithm enabling the runtime verification during the systems execution or simulation. Our approach extends the original framework by considering imprecise signals and by enhancing the logics semantics with the possibility to express partial guarantees about the conformance of the systems behavior with its specification. Finally, we demonstrate our approach in a real-world environmental monitoring case study.
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