Abstract. Models express not only information about their intended domain but also about the way in which the model is incomplete, or "partial". This partiality supports the modeling process because it permits the expression of what is known without premature decisions about what is still unknown, until later refinements can fill in this information. A key observation of this paper is that a number of partiality types can be defined in a modeling language-independent way, and we propose a formal framework for doing so. In particular, we identify four types of partiality and show how to extend a modeling language to support their expression and refinement. This systematic approach provides a basis for reasoning as well as a framework for generic tooling support. We illustrate the framework by enhancing the UML class diagram and sequence diagram languages with partiality support and using Alloy to automate reasoning tasks.

Software product lines and model transformations are two techniques used in industry for managing the development of highly complex software. Product line approaches simplify the handling of software variants while model transformations automate software manipulations such as refactoring, optimization, code generation, etc. While these techniques are well understood independently, combining them to get the benefit of both poses a challenge because most model transformations apply to individual models while modellevel product lines represent sets of models. In this paper, we address this challenge by providing an approach for automatically "lifting" model transformations so that they can be applied to product lines. We illustrate our approach using a case study and evaluate it through a set of experiments.

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