By John Etchemendy (auth.), Gem Stapleton, John Howse, John Lee (eds.)

This publication constitutes the refereed court cases of the fifth foreign convention on idea and alertness of Diagrams, Diagrams 2008, held in Herrsching, Germany, in September 2008.

The 25 revised papers and 28 poster papers awarded including three keynote papers and a couple of instructional papers have been rigorously reviewed and chosen from 70 submissions. The papers are prepared in topical sections on diagram aesthetics and format, mental and cognitive matters, functions of diagrams, theoretical features, diagrams in schooling, in addition to realizing and comprehension.

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Additional info for Diagrammatic Representation and Inference: 5th International Conference, Diagrams 2008, Herrsching, Germany, September 19-21, 2008. Proceedings

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42 A. Fish and J. Flower not well-formed because the zone o is disconnected, but we have included it because it is indicative of a more general kind of behaviour where the disconnecting contours do not form a Venn diagram. The generalisations of Theorem 2 can be proved by induction: Theorem 5. Let d be a concrete Euler diagram. Then the following statements are equivalent: 1. 2. 3. 4. 8 d has an n-disconnecting contour set X ⊆ C(d). X corresponds to a cut vertex set of the intersection graph of d.

This allows the decomposition of concrete Euler diagrams into its prime factors. Furthermore, translations of such a decomposition to the abstract level are provided, thereby allowing the application of the techniques to the Euler diagram generation problem. While the property of nesting is a powerful way to decompose some large diagrams into smaller, more easily drawable, pieces, there remain classes of large diagram which pose problems for drawing algorithms. In this paper we introduce the concept of a disconnecting contour which can be used to split many more large diagrams into smaller diagrams, adding value to all the various existing drawing algorithms.

Section 2 begins with the necessary background notation and definitions for the rest of the paper, including the notion of a concrete Euler diagram, the Euler dual graph and the intersection graph of a concrete Euler diagram. In Section 3 we review work on nested diagrams. The key concepts of disconnecting contours and 1-separating curves are introduced in Section 4, together with theorems relating these concepts with the Euler dual graph. In Section 5 we recall the Euler diagram generation problem and describe an algorithm which uses of disconnecting contours within an existing generation algorithm.

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