Reasoning about Continuous Processes

Overcoming the disadvantages of equidistant discretization of continuous actions, we introduce an approach that separates time into slices of varying length bordered by certain events. Such events are points in time at which the equations describing the system’s behavior—that is, the equations which specify the ongoing processes—change. Between two events the system’s parameters stay continuous. A high-level semantics for drawing logical conclusions about dynamic systems with continuous processes is presented, and we have developed an adequate calculus to automate this reasoning process. In doing this, we have combined deduction and numerical calculus, offering logical reasoning about precise, quantitative system information. The scenario of multiple balls moving in 1-dimensional space interacting with a pendulum serves as demonstration example of our method.