Type-syntax and token-syntax in diagrammatic systems

While it is crucial to understand the formal structure of the semantic domain of an information system, in this paper we raise an ontological issue about the syntactic aspect of a representation system through a case study on a diagrammatic system. The uptake in the software industry of notations for designing systems visually has been accelerated with the standardization of the Unified Modeling Language (UML). The formalization of diagrammatic notations is important for the development of essential tool support and to allow reasoning to take place at the diagrammatic level. Focusing on an extended version of Venn and Euler diagram(which was developed to complement UML in the specification of software systems), this paper presents two levels of syntax for this system: type-syntax and token-syntax. Token-syntax is about particular diagrams instantiated on some physical medium, and type-syntax provides a formal definition with which a concrete representation of a diagram must comply. While these two levels of syntax are closely related, the domains of type-syntax and token-syntax are ontologically independent, that is, one is abstract and the other concrete. We discuss the roles of type-syntax and token-syntax in diagrammatic systems and show that it is important to consider both levels of syntax in diagrammatic reasoning systems and in developing software tools to support such systems.