Proofs for traffic safety - combining diagrams and logic

Due to the increasing interest in autonomously driving cars, safety issues of such systems are of utmost importance. Safety in this sense is primarily the absence of collisions, which is inherently a spatial property. Within computer science, typical models of cars include specifications of their behaviour, where the space a car needs for operating safely is a function of time. This complicates proofs of safety properties tremendously. In this thesis, we present methods to separate reasoning on space from the dynamical behaviour of cars. To that end, we define an abstract model with an emphasis on spatial transformations of the situation on the road. Based on this model, we develop two formalisms: We give the definitions of a modal logic suited to reason about safety properties of arbitrarily many cars. Furthermore, we present a diagrammatic language to ease the specification of such properties. We formally prove that no collisions arise between cars obeying a small set of requirements.