oa Analysing existing set theoretic and program specification diagrams

This research is aimed at evaluating the usability of notational systems that are used for specifying programs. We provide a conceptual analysis of the development of constraint diagrams (CD) as a diagrammatic notation which developed to support program specification. A detailed analysis of multi-case comparisons of formal languages and graphical systems for expressing logic and program constructs was conducted in order to trace how the development of the notations overcame the limitations of earlier generations of notations. By following the evolution of logic diagrams, we consider why and how they have been successively revised to increase their expressivity or their ease of comprehensibility and use. Visualizations of logic were proposed over the centuries. Leonhard Euler presented Euler diagrams, John Venn generalized Euler diagrams and presented Venn diagrams, and Charles Peirce extended Venn diagrams by increasing their expressiveness and presented Venn-Peirce diagrams. The modifications from Peirce to Shin concentrate on restoring visual clarity, but without loss of expressive power. Based on that, Constraint Diagrams were presented by Stuart Kent for constraint specification, behavioural specification, and relational navigation. We found that the gradual changes in diagrams from Euler Circles through Venn, Peirce, Shin to Constraint Diagrams share three complementary common themes: (1) to increase the expressiveness, (2) to increase the logical power of the formality of the system, and (3) to enhance the visual clarity. Depending on the purpose of designing a diagram, the priority of a theme over other themes is granted. For example, both Venn and Peirce adopted the same kind of solution in order to achieve these improvements: to introduce new syntactic objects, that is, shadings by Venn, and x's, o's, and lines by Peirce. However, on the negative side, these revised systems suffer from a loss of visual clarity, mainly because of the introduction of more arbitrary conventions. The modifications from Peirce to Shin concentrate on restoring visual clarity, but without loss of expressive power. The extension from these diagrams resulted in CD, which allows relational navigation (expressions involving two place predicates), is more expressive than previous diagrams, and has higher visual clarity and logical power.