Towards a mathematical concept of a component and its use

We deal with the concept of a component, considered as a black box that is a physical encapsulation of related services according to a published specification. These services can only be accessed through a consistent and published interface that includes an interaction standard. Such a notion of a component needs a carefully chosen semantic concept of a syntactic and a semantic interface that allows us to provide a precise, unambiguous published specification. We present a mathematical model for the interface of components. We demonstrate its use for the modelling of software architectures, interoperability between components, and the process of incremental systems and software development.