Differential-Algebraic Dynamic Logic DAL

We generalise dynamic logic to a logic for differential-algebraic programs, i.e., discrete programs augmented with first-order differential-algebraic formulas as continuous evolution constraints in addition to first-order discrete jump formulas. These programs characterise interacting discrete and continuous dynamics of hybrid systems elegantly and uniformly, including systems with disturbance and differential-algebraic equations. For our logic, we introduce a calculus over real arithmetic with discrete induction and a new differential induction with which differential-algebraic programs can be verified by exploiting their differential constraints algebraically without having to solve them.We develop the theory of differential induction and differential refinement and analyse their deductive power. As an example, we present parametric tangential roundabout manoeuvres in air traffic control and prove collision avoidance in our calculus.

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