Spider diagram

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

For the British English use of "spidergram" and "spidergraph", see mind map.

A unitary 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. The origin of the word spider diagram comes from the word spider. The diagram has many legs just like a spider.

$A \land B$

$B \land C$

$F \land E$

$G \land F$

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

A spider diagram is a unitary spider diagram or the conjunction of two spider diagrams or the disjunction of two spider diagrams or the negation of a spider diagram. That is to say we may form boolean expressions involving unitary spider diagrams and the logical symbols $\land,\lor,\lnot$.

The spider diagram logic is expressively equivalent to monadic first order logic with a binary equality relation.

Spider diagrams are often used in Mind Maps

References

• Howse, J. and Stapleton, G. and Taylor, J. Spider Diagrams London Mathematical Society Journal of Computation and Mathematics, (2005) v. 8, pp. 145–194. ISSN 1461-1570 Accessed on January 8, 2012 here

• 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 January 4, 2012 here

• Stapleton, G. and Jamnik, M. and Masthoff, J. On the Readability of Diagrammtic Proofs Proc. Automated Reasoning Workshop, 2009, Accessed on January 22, 2010. here

External links

• Brighton and Kent University - Euler Diagrams