  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 system's 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 node's 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 system's 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 system's behavior with its
specification. Finally, we demonstrate our approach in a real-world
environmental monitoring case study.
