| Models are invariably used in Engineering (for design) and Science (for analysis) to precisely describe structure as well as behaviour of systems.Models may have components described in different formalisms, and may span different levels of abstraction. In addition, models are frequently transformed into domains/formalisms where certain questions can be easily answered. We introduce the term “multiparadigm modelling” to denote the interplay between multi-abstraction modelling, multi-formalism modelling and the modelling of model transformations.
The foundations of multi-paradigm modelling will be presented. It will be shown how all aspects of multiparadigm modelling can be explicitly (meta-)modeled enabling the efficient synthesis of (possibly domain-specific) multi-paradigm (visual) modelling environments.We have implemented our ideas in the tool AToM3 (A Tool for Multi-formalism and Meta Modelling) [3].
Over the last decade, Equation-based Object-Oriented Languages (EOOLs) have proven to bring modelling closer to the problem domain, away from the details of numerical simulation of models. Thanks to Object-Oriented structuring and encapsulation constructs, meaningful exchange and re-use of models is greatly enhanced.
Different directions of future research, combiningmultiparadigm modelling concepts and techniques will be explored:
1. meta-modelling and model transformation for domainspecific modelling as a layer on top of EOOLs;
2. on the one hand, the use of Triple Graph Grammars (TGGs) to declaratively specify consistency relationships between different models (views). On the other hand, the use of EOOLs to complement Triple Graph Grammars (TGGs) in an attempt to come up with a fully “declarative” description of consistency between models to support co-evolution of models;
3. the use of graph transformation languages describing structural change to modularly “weave in” variable structure into non-dynamic-structure modelling languages. | 
Ph.D., Lic. Theses
