Specifying and Monitoring Properties of Stochastic Spatio-Temporal Systems in Signal Temporal Logic

Abstract

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.

A calculus for collective-adaptive systems and its behavioural theory

“…Thus, we would like to investigate the impact of spatio-temporal logic approaches in the context of AbC models. One promising approach is presented in [28].…”

A Logic Language for Run Time Assessment of Spatial Properties in Self-Organizing Systems

“…[3] defines a spatial logic used to formalize topological properties verifiable through a model checker. In [4], an extension of Signal Temporal Logic is proposed to verify properties in continuous-time, discrete-space systems. Design time techniques (e.g.…”

“…Design time techniques (e.g. [4]) evaluate formulae offline, resorting to statistical system parameters (such as transition probabilities among spatial locations) usually obtained through stochastic simulations or to numerical integrations. The second category contains methodologies and techniques used at run time to deduct the emergence of a specific global behavior on the basis of some pattern behaviors appearing in the system (e.g.…”

Location Aggregation of Spatial Population CTMC Models

“…Spatial extensions of PCTMCs typically introduce discrete representations of space in terms of locality, connecting them in a general topology represented by a (weighted) graph [7]. One of the effects of explicit modelling of space is the increase of the computational cost of analysis of the system.…”