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Euler diagram
From Wikipedia, the free encyclopedia
An Euler diagram is a way of representing how sets overlap - similar to the more commonly-known Venn Diagram.
It is named after its inventor Leonhard Euler[1]. Unlike a Venn diagram, it does not have to contain all possible zones (where a zone is defined as the area of intersection of the sets its shows. Thus, an Euler diagram can define a universe of discourse, i.e. it can define a system whereby certain intersections are not possible or are taken as agreed as not necessary to be considered, and therefore need not be shown on the diagram. In other words, the Euler diagram can represent degenerate conjunctions.
A Venn Diagram, on the other hand, shows all possible combinations of conjunctions. A VD for the system above would show the "unconsidered" zone and, if necessary, mark it specially. Thus, a Venn diagram containing the attributes for Animal, and Mineral would have to contain an intersection where something was both animal and mineral - even though all readers would know that this intersection was impossible (i.e. known to be empty simply by the definition of "Animal" and "Mineral").
A modern extension to Euler diagrams, is the spider diagram, whereby existential points are added to the diagram, which can be linked. This gives the diagrams a disjunctive aspect. The diagrams already have a conjunctive aspect (i.e. a zone defines that the existence of an object in the zone has the attributes 'ANDed' together). The spider diagram thus allows logical OR conditions to be modelled with an Euler diagram.