Time, Abstraction, Causality and Modularity in Interactive Systems: Extended Abstract

We study discrete models of interactive distributed systems structured into components and operating concurrently in a time frame. For such models of the data or signal flow in interactive system we assume that there is a source and a cause for each communication event and its associated information. To understand the logical dependencies for the events of systems causality is a key issue for reasoning about the event flow. Being interested in a structured modular approach we want to be able to abstract away all internal aspects of systems that are used as components within a system’s architecture. We speak of interface abstraction. The interface abstraction is to keep only the aspects relevant for the usage of the component and the construction of the interface abstraction of the architecture. We speak of modularity if the interface abstraction of an architecture is the result of the composition of the interface abstractions of all its components. In particular, we discuss and study the relationship and dependencies between causality, input and output, compositionality, and the granularity of time.