A Hyperdense Semantic Domain for Discontinuous Behavior in Physical System Models

Multiple time models have been proposed for the formaliza- tion of hybrid dynamic system behavior. The superdense notion of time is a well-known time model for describing event-based systems where sev- eral events can occur simultaneously. Hyperreals provide a domain for defining the semantics of hybrid models that is elegantly aligned with first principles in physics. This paper discusses the value of both time models and shows how approximating di↵erent physical e↵ects is best expressed over di↵erent domains. Finally, the formalization and interac- tion of two types of discontinuities observed in hybrid systems, mythical modes and pinnacles, are explored. This analysis helps specify seman- tics that combine continuous-time behavior with discontinuities in the computational system.