Theories of Diagrammatic Reasoning: Distinguishing Component Problems
Minds and Machines
On the Completeness and Expressiveness of Spider Diagram Systems
Diagrams '00 Proceedings of the First International Conference on Theory and Application of Diagrams
IJCAI'71 Proceedings of the 2nd international joint conference on Artificial intelligence
Machine Graphics & Vision International Journal - Special issue on diagrammatics & Design
Vivid: A framework for heterogeneous problem solving
Artificial Intelligence
Abstractions of Euler Diagrams
Electronic Notes in Theoretical Computer Science (ENTCS)
The semantics of augmented constraint diagrams
Journal of Visual Languages and Computing
Efficient on-line algorithms for Euler diagram region computation
Computational Geometry: Theory and Applications
Twelve years of diagrams research
Journal of Visual Languages and Computing
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Diagrams have many uses in mathematics, one of the most ambitious of which is as a form of proof. The domain we consider is real analysis, where quantification issues are subtle but crucial. Computers offer new possibilities in diagrammatic reasoning, one of which is animation. Here we develop animated rules as a solution to problems of quantification. We show a simple application of this to constraint diagrams, and also how it can deal with the more complex questions of quantification and generalisation in diagrams that use more specific representations. This allows us to tackle difficult theorems that previously could only be proved algebraically.