Guiding and refining simulation using temporal logic

Abstract

We illustrate TeQSIM, a qualitative simulator for continuous dynamical systems. It combines the expressive power of qualitative differential equations with temporal logic by interleaving simulation with model checking to constrain and refine the resulting predicted behaviors. Temporal logic expressions are used to specify constraints that restrict the simulation to a region of the state space and to specify trajectories for input variables. A propositional linear-time temporal logic is adopted, which is extended to a three valued logic that allows a formula to be conditionally entailed when quantitative information specified in the formula can be applied to a behavior to refine it. The authors present a formalization of the logic with theoretical results concerning the adopted model checking algorithm (correctness and completeness). They show also an example of the simulation of a non-autonomous dynamical system and illustrate possible application tasks, ranging from simulation to monitoring and control of continuous dynamical systems, where TeQSIM can be applied.