We present an extension of the linear time, time-bounded, Signal Temporal Logic to describe spatio-temporal properties. We consider a discrete location/ patch-based representation of space, with a population of interacting agents evolving in each location and with agents migrating from one patch to another one. We provide both a boolean and a quantitative semantics to this logic. We then present monitoring algorithms to check the validity of a formula, or to compute its satisfaction (robustness) score, over a spatiotemporal trace, exploiting these routines to do statistical model checking of stochastic models. We illustrate the logic at work on an epidemic example, looking at the diffusion of a cholera infection among communities living along a river. ological ones [24] , and in the design of new systems [5] . This is due to their ability to easily express complex temporal behavioural patterns, and the availability of efficient model checking and monitoring tools, for many classes of mathematical models, ranging from ODEs [28] to stochastic processes [4, 5] .
In REF , an extension of Signal Temporal Logic is proposed to verify properties in continuous-time, discrete-space systems.
Specifying and Monitoring Properties of Stochastic Spatio-Temporal Systems in Signal Temporal Logic
VALUETOOLS
Computer Science