A Sequent Calculus for First-Order Dynamic Logic with Trace Modalities

A Temporal Dynamic Logic for Verifying Hybrid System Invariants

“…Future work includes extending dTL with CTL * -like [11] formulas of the form [α](ψ ∧ φ) to avoid splitting of the proof into two very similar sub-proofs for temporal parts [α] φ and nontemporal parts [α]ψ arising in T1. Our combination of temporal logic with dynamic logic is more suitable for this purpose than the approach in [4], since dTL has uniform modalities and uniform semantics for temporal and non-temporal specifications. This extension will also simplify the treatment of alternating liveness quantifiers conceptually.…”

“…Continuous phases are governed by differential equations, whereas discontinuities are caused by discrete jumps in state space. Unlike in discrete cases [4,25], traces are not just sequences of states, since hybrid systems pass through uncountably many states even in bounded time. Beyond that, continuous changes are more involved than in pure real-time [1,15], because all variables can evolve along different differential equations.…”

“…Beckert and Schlager [4] say they failed to find sound rules for a discrete case that corresponds to [α; γ]♦φ.…”

“…Based on [25], Beckert and Schlager [4] added separate trace modalities to dynamic logic and presented a relatively complete calculus. Their approach only handles discrete state spaces.…”

“…Our calculus directly supports verification of hybrid programs with first-order definable flows; first-order approximations of more general flows can be used according to [23]. First-order DL is more expressive and calculi are deductively stronger than other approaches [4,17].…”