Constraint diagram reasoning

Diagrammatic human-computer interfaces are now becoming standard. In the near future, diagrammatic front-ends, such as those of UML-based CASE tools, will be required to offer a much more intelligent behavior than just editing. Yet there is very little formal support and there are almost no tools available for the construction of such environments. The present paper introduces a constraint-based formalism for the specification and implementation of complex diagrammatic environments. We start from grammar-based definitions of diagrammatic languages and show how a constraint solver for diagram recognition and interpretation can automatically be constructed from such grammars. In a second step, the capabilities of these solvers are extended by allowing to axiomatise formal diagrammatic systems, such as Venn Diagrams, so that they can be regarded as a new constraint domain. The ultimate aim of this schema is to establish a language of type CLP(Diagram) for diagrammatic reasoning applications.