Spider diagram

In mathematics, 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. Joined points represent an "or" condition, also known as a logical disjunction.

A spider diagram is a boolean expression involving unitary spider diagrams and the logical symbols $\land ,\lor ,\lnot$. For example, it may consist of the conjunction of two spider diagrams, the disjunction of two spider diagrams, or the negation of a spider diagram.

Example

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

References

• Howse, J. and Stapleton, G. and Taylor, H. 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 Diagrammatic Proofs Proc. Automated Reasoning Workshop, 2009. PDF

External links

• Brighton and Kent University - Euler Diagrams