Highlights on Logic of Autonomous Dynamical Systems

KeYmaera X

Mon, 01 Jan 0001 00:00:00 +0000

KeYmaera X is a theorem prover for differential dynamic logic (dL), a logic for specifying and verifying properties of hybrid systems with mixed discrete and continuous dynamics. Reasoning about complicated hybrid systems requires support for sophisticated proof techniques, efficient computation, and a user interface that crystallizes salient properties of the system. KeYmaera X allows users to specify custom proof search techniques as tactics, execute tactics in parallel, and interface with partial proofs via an extensible user interface. KeYmaera X also is a verification tool for differential game logic (dGL), a logic for specifying and verifying properties of hybrid games with mixed discrete, continuous and adversarial dynamics.

Differential Dynamic Logic

Mon, 01 Jan 0001 00:00:00 +0000

Differential dynamic logic (dL) is a logic for specifying and verifying hybrid systems combining discrete and continuous dynamical systems. Such hybrid systems combine discrete dynamics, e.g., for representing the instantaneous change of computer decisions with continuous dynamics represented as differential equations, e.g., for the continuous motion of a car or aircraft. The purpose of dL is that this logic can be used to describe/specify and prove/verify correctness properties for hybrid systems given operationally as hybrid programs using the dL proof calculus. The logic dL and its proof calculus are the basis of the deductive verification tool KeYmaera for hybrid systems and its successor KeYmaera X. In addition, the hybrid systems and correctness properties formulated in dL may include symbolic parameters, which can be free or quantified to discover the required parametric safety constraints.

Logical Foundations of CPS

Mon, 01 Jan 0001 00:00:00 +0000

Cyber-physical systems (CPSs) combine cyber capabilities, such as computation or communication, with physical capabilities, such as motion or other physical processes. Cars, aircraft, and robots are prime examples, because they move physically in space in a way that is determined by discrete computerized control algorithms. Designing these algorithms is challenging due to their tight coupling with physical behavior, while it is vital that these algorithms be correct because we rely on them for safety-critical tasks.

Semi-competitive differential game logic

Mon, 01 Jan 0001 00:00:00 +0000

Semi-competitive differential game logic (dGLsc) is a logic for verifying two-player non-zero sum games where both players have an individual goal. The players behave semi-competitively, i.e. they help each other where possible and compete where necessary. Thus, dGLsc addresses the challenge that even though each player may benefit from knowledge of the other player’s goals, e.g., concerning shared safety objectives, unsafety might still arise if every player were to mutually assume the other player would act to avoid unsafety. The logic is therefore particularly well suited to verify, for example aerial collision avoidance with the dGLsc proof calculus.