Verification of temporal logic properties plays a crucial role in proving the desired behaviors of hybrid systems. In this paper, we propose an interval method for verifying the properties described by a bounded linear temporal logic. We relax the problem to allow outputting an inconclusive result when verification process cannot succeed with a prescribed precision, and present an efficient and rigorous monitoring algorithm that demonstrates that the problem is decidable. This algorithm performs a forward simulation of a hybrid automaton, detects a set of time intervals in which the atomic propositions hold, and validates the property by propagating the time intervals. A continuous state at a certain time computed in each step is enclosed by an interval vector that is proven to contain a unique solution. In the experiments, we show that the proposed method provides a useful tool for formal analysis of nonlinear and complex hybrid systems.
 In this paper we introduce a variant of temporal logic tailored for specifying desired properties of continuous signals. The logic is based on a bounded subset of the real-time logic mitl, augmented with a static mapping from continuous domains into propositions. From formulae in this logic we create automatically property monitors that can check whether a given signal of bounded length and finite variability satisfies the property. A prototype implementation of this procedure was used to check properties of simulation traces generated by Matlab Simulink. 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.