Towards Hilbertian Formal Methods

In this work, we address the issue of handling complex continuous evolutions of the environment of embedded systems. There is now an impressive amount of research in the area of intelligent embedded controllers, and thus we do not need to argue about the importance of this subject. Our contribution is twofold: 1. define a new problem, that of using complex mathematical information about continuous environments; and 2. propose an initial solution in the form of a new logic defined using Hilbertian methods. This represents the first step towards using abstract continuous mathematics in formal methods, a program that we have called Hilbertian formal methods.