Qualitative Simulation and Temporal Logic: Proving Properties of Continuous Systems

We demonstrate an automated method for proving statements in temporal logic about continuous systems, even in the face of incomplete knowledge. The method combines an implemented, on-they , model-checking algorithm for statements in the temporal logic CTL* 3, 4, 5] with the output of the qualitative simulation algorithm QSIM 10, 12]. Based on the QSIM Guaranteed Coverage Theorem, we prove that for certain CTL* statements, , if is true for the qualitative behavior tree produced by QSIM, then a corresponding theorem holds for the solution of any ordinary diierential equation consistent with the qualitative diierential equation that generated the QSIM behavior tree. We then show that for other CTL* formulas, if the QSIM output satisses a certain completeness restriction , then conclusions can again be drawn about real-valued functions satisfying the given incomplete description. We also show how the methods can be applied to proving properties of continuous systems in which numeric information is available.