Get Diagrammatic Representation and Inference: 5th International PDF

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

This ebook constitutes the refereed court cases of the fifth overseas convention on thought and alertness of Diagrams, Diagrams 2008, held in Herrsching, Germany, in September 2008.

The 25 revised papers and 28 poster papers offered including three keynote papers and a couple of instructional papers have been conscientiously reviewed and chosen from 70 submissions. The papers are geared up in topical sections on diagram aesthetics and format, mental and cognitive concerns, purposes of diagrams, theoretical facets, diagrams in schooling, in addition to knowing and comprehension.

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

Example text

4 Planar Layout In this step we embed the dual graph in the plane. There are various standard approaches to planar layout. At the moment we use a method provided by the ODGF software library. We make one adjustment to ensure the node labelled with “∅” is in the outer face of the drawn graph, as this node represents the part of the diagram enclosed by no contour. The layout of the dual has a significant impact on the drawing of the diagram, and Section 3 includes some discussion of methods to layout planar graphs to improve the usability of the final diagram.

Then C ∈ C(d) is a disconnecting contour if and only if there exists a cut pair 4 {v1 , v2 } in the Euler dual graph where the label set of v1 differs from the label set of v2 by precisely the label of C. Proof. Firstly, suppose that C is a disconnecting contour of d. Then there exists p which is a 1-separating curve for C by Theorem 2. The curve p induces a cycle in the Euler dual graph. Since C is a disconnecting contour, the cycle induced by p is a cut-cycle. Furthermore, since p is a 1-separating curve it also only meets contour C in d.

A particularly nice case of the semantics is when a disconnecting contour C of a diagram d “splits every zone of d − C in two”. For example, in the right hand side of Figure 6 the contour E is a disconnecting contour and it splits every zone of d − E in two. The effect of splitting every zone of d − E in two is that we can use the same associated semantic statement for d as for the nested diagram d − E, that is A ∪ B ⊆ D ∩ C. The first diagram of Figure 7 has two disconnecting contours, E and F .

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