Abstract Metric first-order temporal logic (MFOTL) is an expressive formalism for specifying temporal and data-dependent constraints on streams of time-stamped, data-carrying events. It serves as the specification language of several runtime monitors. These monitors input an MFOTL formula and an event stream prefix and output satisfying assignments to the formula’s free variables. For complex formulas, it may be unclear why a certain assignment is output. We propose an approach that accompanies assignments with detailed explanations, in the form of proof trees. We develop a new monitor that outputs such explanations. Our tool incorporates a formally verified checker that certifies the explanations and a visualization that allows users to interactively explore and understand the outputs.

We formally introduce IsaVODEs (Isabelle verification with Ordinary Differential Equations), an open, compositional and extensible framework for the verification of cyber-physical systems. We extend a previous semantic approach with methods and techniques that increase its expressivity, proof automation, and scalability to the level of state-of-the-art deductive verification tools. Our contributions include a user-friendly specification language, a flexible hybrid store model, including vectors and matrices, and separation-logic-style rules for local reasoning with hybrid stores using a novel form of differentiation called framed Fréchet derivatives. The formalisation of correctness specifications with forward predicate transformers, the certification of flows as unique solutions to systems of ordinary differential equations, and invariant reasoning for such systems also contribute to the scalability and usability of our framework. In combination, these features make our framework flexible and adaptable to several verification workflows. A suite of examples and hybrid systems verification benchmarks validate our framework relative to other state-of-the-art approaches.

Abstract We present a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL. It supports reasoning about the temporal evolutions of hybrid programs in the style of differential dynamic logic modelled by flows or invariant sets for vector fields. We introduce the semantic foundations of this framework and summarise their Isabelle formalisation as well as the resulting verification components. A series of simple examples shows our approach at work.