Meta-Modeling

In DPF, we utilize categories of typed graphs, i.e., slice categories, to define the semantics of sketches. This enabled us to formalize arbitrary deep modeling hierarchies in a quite straightforward way. In this paper, we follow the tradition in logic and work with a Tarskian semantics of sketches, i.e., we work with functor categories instead of slice categories. This makes the formalization of modeling hierarchies rather involved.

Meta-modeling is a big topic on its own and, at the present stage, we are not capable of providing a detailed analysis and treatment of meta-modeling in Logics of Statements. The examples are, however, designed in such a way that we can, at least, point at the meta-modeling issue. We have to include, nevertheless, meta-modeling is an important item on our overall wish list:

Objective 4: The framework enables us to address and formalize meta-modeling.
