REGION COMPUTATIONS FOR EULER DIAGRAMS WITH RELAXED CONSTRAINTS

Euler diagrams are an accessible and e?ective visualisation of data involving simple set-theoretic relationships. Tool support often requires access to the abstract model to operate on; for example, when considering interpretations of drawn diagrams the semantic function is applied to the abstract model, or when considering diagrammatic logics, inference rules are applied to the abstract model. In interactive settings, the system needs to update the abstract model in accordance with user interactions. Therefore, the efficient computation of the abstract model from a given concrete diagram, together with the ability to update the abstract model upon concrete changes such as contour addition or removal, represents an important challenge to be addressed. Recently, on-line algorithms which quickly compute the regions of a given wellformed (weakly reducible) Euler diagram have been developed. However, there are many occasions when relaxing some of the wellformedness conditions, particularly the connectedness of zones condition, can be beneficial. For example, for the user construction of wellformed diagrams, if the user is allowed to construct intermediary non-wellformed diagrams then this aids them in adopting a natural construction method. We extend the algorithms for on-line automatic region computation to allow for the relaxation of wellformedness conditions, including the connectedness of zones, enabling a greater flexibility for users of future software tools which realise this theory in practise.

Peoples Links
  Rosario De Chiara
  Andrew Fish
  Gennaro Cordasco
  Source .ZIP
Use the left Mouse Button and drag to draw a new Ellipse. While dragging, use the wheel to change the size of the minor axes. Release the button to add the Ellipse.
If the current diagram is not well formed the diagram is depicted in red and disconnected zones are orange. Intersection point (magenta) and Marking point (green) are always showed.
  • Use the right mouse button on an Ellipse contour to delete the selected Ellipse
  • Use the center mouse button to emphasize (white) a zone and all its intersection points (green).
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