Playing Hybrid Games with KeYmaera

  • Jan-David Quesel
  • André Platzer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7364)


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.


differential dynamic logic hybrid games sequent calculus theorem proving logics for hybrid systems factory automation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jan-David Quesel
    • 1
  • André Platzer
    • 2
  1. 1.Department of Computing ScienceUniversity of OldenburgGermany
  2. 2.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA

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