Studies of Euler diagrams/criteria

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This project aims to automatically find Euler diagrams that meet the criteria listed below.

When the dimension required for the perfect Euler diagram is too high, one can relinquish some criteria to find a useful diagram.

Only the completeness of spots and links should be considered essential.


completeness of spots[edit | edit source]

A fullspot is a true bit of the Boolean function.
Every fullspot must be represented by a cell.


completeness of links[edit | edit source]

A link is the connection between neighboring spots. In an Euler diagram it is a wall between two cells.
Every pair of fullspots with a Hamming distance of 1 must be represented by a wall between cells.


contiguousness of spots and links[edit | edit source]

A fullspot should be represented by exactly one contiguous cell. A link should be represented by exactly one contiguous wall between cells.


contiguousness of borders[edit | edit source]

All links corresponding to the same atom should form one contiguous border.


connectedness[edit | edit source]

All fullspots must be connected by links. This can require the insertion of gapspots.   (The dual of the Euler diagram must be a connected graph.)


incrementality[edit | edit source]

Every link changes exactly one bit. (Thus every link corresponds to one atom.)


non-arbitrariness[edit | edit source]

Arbitrary choices should generally be avoided. Spots that have the same properties in a Venn diagram or hypercube should also have the same properties in the Euler diagram.
This is mostly about the choice of gapspots, but not only (as the vidita example shows.)