Spider diagram

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This article is about the extension of Euler diagrams. For other uses, see semantic maps.

A spider diagram adds existential points to an Euler or a Venn diagram. The points indicate the existence of an attribute described by the intersection of contours in the Euler diagram. These points may be joined together forming a shape like a spider. These represent an OR condition, also known as a logical disjunction.

Logical disjunction superimposed on Euler diagram

In the image shown, the following conjunctions are apparent from the Euler diagram.

$A \land B$

$B \land C$

$F \land E$

$G \land F$

In the universe of discourse defined by this Euler diagram, in addition to the conjunctions specified above, all possible sets from A through B and D through G are available separately. The set C is only available as a subset of B. Often, in complicated diagrams, singleton sets and/or conjunctions may be obscured by other set combinations.

The two spiders in the example correspond to the following logical expressions:

Red spider: $(F \land E) \lor (G) \lor (D)$

Blue spider: $(A) \lor (C \land B) \lor (F)$

[edit] Further information

Spider diagrams are not widely accepted mathematical tools within either the UK or the US^{[citation needed]}.

They may be related to UML or OCL (there are a few publications detailing the software based applications of spider diagrams – though UML is held as being far more widely accepted and is already an industry standard for the purposes of aiding software modelling).

Mathematicians with what might be termed a traditional mathematical background do not study the body of knowledge associated with Spider Diagrams (perhaps out of intellectual predjudice - or just a genuine desire to know that mathematics which has found various forms of practical application and wide recognition?).

To some mathematicians at least, it is difficult to see how spider diagrams could be likened in mathematical validity or applicability to algebraic topology, combinatorics, partial differential equations or, indeed, other widely accepted branches of mathematical study which have already found tried and tested practical applications within the wider world - and, as such, are intensely studied despite being well-established.

There are no textbooks that relate to spider diagram based research and it is not widely taught to undergraduates within either the US or the UK^{[citation needed]}.

Several papers have been published within the area of Spider diagrams. At least one mathematician has questioned the validity of this area of mathematical research^{[citation needed]}.

[edit] External links

Brighton and Kent University - Euler Diagrams

[edit] References

Stapleton, G. and Howse, J. and Taylor, J. and Thompson, S. What can spider diagrams say Proc. Diagrams, (2004) v. 168, pgs 169-219 Accessed on May 17, 2007 here