Reasoning with Projected Contours

Projected contours enable Euler diagrams to scale better. They enable the representation of information using less syntax and can therefore increase visual clarity. Here informal reasoning rules are given that allow the transformation of spider diagrams with respect to projected contours. 1 Spider diagrams and projected contours A spider diagram [3] is an Euler diagram with plane trees (spiders) that represent the existence of elements and shading in regions that indicate upper bounds on the cardinalities of sets they denote. Projected contours [1, 2] here are dashed and non-projected contours are called given contours. The semantics of projected contours are given in [1]: a projected contour represents the intersection of the set denoted by its label with the set denoted by its context (the smallest region, defined in terms of given contours, that it intersects).