Playing Hybrid Games with KeYmaera

We propose a new logic, called differential dynamic game logic (${\sf dDG}{\mathcal{L}}$), that adds several game constructs on top of differential dynamic logic (${\sf d}\mathcal{L}$) so that it can be used for hybrid games. The logic ${\sf dDG}{\mathcal{L}}$ is a conservative extension of ${\sf d}\mathcal{L}$, which we exploit for our implementation of ${\sf dDG}{\mathcal{L}}$ in the theorem prover KeYmaera. We provide rules for extending the ${\sf d}\mathcal{L}$ sequent proof calculus to handle the ${\sf dDG}{\mathcal{L}}$ constructs by identifying analogs to operators of ${\sf d}\mathcal{L}$. We have implemented ${\sf dDG}{\mathcal{L}}$ in an extension of KeYmaera and verified a case study in which a robot satisfies a joint safety and liveness objective in a factory automation scenario, in which the factory may perform interfering actions independently.