Algebraic semantics for object-oriented modelling

There are several object-oriented analysis and modeling techniques available today. They differ in notation and their methodological framework. But their conceptional kernel is always the same: classes, objects, relationships, inheritance, aggregation, etc. Hence it is worthwhile to study the semantics of those concepts independently of any concrete notation. We do that in this paper on the basis of graph grammars, which provide a semantical fundament for both static and dynamic aspects of these modeling techniques: Static aspects are modeled by suitable signatures, so called graph signatures, states conforming to the static structure are given by algebra's (resp. graphs) wrt. graph signatures and dynamic aspects, i.e. state changes can be modeled by algebraic graph transformation rules over these signatures. Thus algebraic graph transformation provides a comprehensive semantics for structural and behavioral aspects of objectoriented models. This paper is self-contained, introduces all technical preliminaries the semantics and illustrates the concepts and their semantics by means of a running example, a small model for an ecological information system.