  The behaviour of systems characterised by a closed interaction of software
components with the environment is inevitably subject to perturbations and
uncertainties. In this paper we propose a general framework for the
specification and verification of requirements on the behaviour of these
systems. We introduce the Evolution Temporal Logic (EvTL), a stochastic
extension of STL allowing us to specify properties of the probability
distributions describing the transient behaviour of systems, and to include the
presence of uncertainties in the specification. We equip EvTL with a robustness
semantics and we prove it sound and complete with respect to the semantics
induced by the evolution metric, i.e., a hemimetric expressing how well a
system is fulfilling its tasks with respect to another one. Finally, we develop
a statistical model checking algorithm for EvTL specifications. As an example
of an application of our framework, we consider a three-tanks laboratory
experiment.
