DisTL: A Temporal Logic for the Analysis of the Expected Behaviour of Cyber-Physical Systems

The behaviour of systems characterised by a closed interaction of software components with the environment is inevitably subject to uncertainties. We propose a general framework for the specification and verification of requirements on the behaviour of these systems. We introduce the Distribution Temporal Logic (DisTL), a novel temporal logic allowing us to specify properties on the expected behaviour of systems, and to include the presence of uncertainties in the specification. We equip DisTL with a robustness semantics and we prove it sound and complete w.r.t. 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 give a statistical model checking algorithm for DisTL specifications, and we apply our framework to a simple unmanned ground vehicle scenario.