First-Order Dynamic Logic
CONCUR '99 Proceedings of the 10th International Conference on Concurrency Theory
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics
Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics
Stochastic differential dynamic logic for stochastic hybrid programs
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Crossing the bridge between similar games
FORMATS'11 Proceedings of the 9th international conference on Formal modeling and analysis of timed systems
Specifications for decidable hybrid games
Theoretical Computer Science
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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.