We like to note that our approach has no restrictions about the ordering of input and the type of allowed relations if we incorporate concrete domains. We do not rely on special parsing techniques since our approach is purely declarative. We can even deal with ambiguous grammars since the DL realizer can compute every model satisfying the specifications. A problem with our approach could be the worst-case time complexity of the underlying classification algorithms. However, almost every logical or constraint approach with an interesting expressiveness has to deal with tractability and decidability. It is also important to note that complexity issues of DLs are well understood and analyzed. A forthcoming paper will investigate these properties and and try to apply them to building a taxonomic hierarchy of visual notations/languages.
We are currently investigating the suitability of our approach for several visual languages and notations (e.g. venn diagrams, petri nets, flow charts, etc). This investigation is facilitated by our generic editor [5] whose semantics are based on our DL theory. We are planning to incorporate description logics with concrete domains over the algebra of simple reals. The relationship between constraint approaches and description logics with concrete domains has to be more thoroughly analyzed.