Proving Properties of Continuous Systems: Qualitative Simulation and Temporal Logic

We demonstrate an automated method for proving temporal logic statements about solutions to ordinary differential equations (ODEs), even in the face of an incomplete specification of the ODE. The method combines an implemented, on-the-fly, model-checking algorithm for statements in the temporal logic CTL* [3, 7, 8] with the output of the qualitative simulation algorithm QSIM [13, 16]. Based on the QSIM Guaranteed Coverage Theorem, we prove that for certain CTL* statements, ~), if ~ is true for the temporal structure produced by QSIM, then a corresponding temporal statement, ~'', holds for the solution of any ODE consistent with the qualitative differential equation (QDE) that QSIM used to generate the temporal structure.