Discrete and Continuous Time in Physical Systems

We investigate the relationship between discrete and continuous time in dynamic physical systems. Employing the common-sense picture behind derivatives, differential equations are translated into discrete-time analogues. The properties of qualitative simulation in discrete time are discussed. It is flirthennore shown that discrete time can be embedded in continuous time in a natural way without the need to introduce the notion of infinitesimals. This provides a new perspective on the extended prediction problem. In addition, it is demonstrated that qualitative differential equations (QDEs) are abstractions not only of ordinary differential equations (ODEs), but also of an important class of integro-differential equations (IDEs). This extends qualitative simulation to the realm ofIDEs.