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We propose the Robustness Temporal Logic (RobTL), a novel temporal logic for the specification and analysis of distances between the behaviours of Cyber-Physical Systems (CPSs) over a finite time horizon. Differently from classical temporal logic expressing properties on the behaviour of a system, we can use RobTL specifications to measure the differences in the behaviours of systems with respect to various objectives and temporal constraints, and to study how those differences evolve in time. Since the behaviour of CPSs is inevitably subject to uncertainties and approximations, we show how the unique features of RobTL allow us to specify property of robustness of systems against perturbations, i.e., their capability to function correctly even under the effect of perturbations. Given the probabilistic nature of CPSs, our model checking algorithm for RobTL specifications is based on statistical inference. As an example of an application of our framework, we consider a supervised, self-coordinating engine system that is subject to attacks aimed at inflicting overstress of equipment.