Formal issues in languages based on closed curves

Three important questions arise when using visual languages: for any given piece of information can we draw a diagram representing that information, can we reliably interpret the diagrams and can we reason diagrammatically about that information? The desirable answer to all three questions is yes, but these desires are often conflicting; for example, well-formedness conditions can be enforced to assist diagram interpretation but this can result in drawability problems. In this paper, we focus on visual languages based on closed curves, which are used in numerous computing applications. Many such languages effectively use spatial properties such as containment and disjointness. We consider the consequences of enforcing various well-formedness conditions, such as simplicity and connectedness of minimal regions, in relation to the above questions. We suggest refinements of the conditions in order to find a balance between the conflicting desires.