Visualization vs. Specification in Diagrammatic Notations: A Case Study with the UML

It is useful to see a notation as a visualization on the top of specification core. The latter deals with semantic meaning of notational constructs while the former is about its presentation (a user interface to specification). In the paper, this general paradigm is applied to a few major constructs used in the UML class diagrams: various sorts of associations between classes, including multi-ary and qualified. A key peculiarity of the approach is that semantic meaning of notational constructs is also specified in a graphical (yet formal) language – the language of generalized sketches adapted from category theory. Then an UML class diagram appears as a visual abbreviation of semantic sketch hidden in it. By comparing two graphical images – the diagram and the sketch – one can analyze the UML notational mechanism and correct it towards better presentation of the intended semantic meaning.