spider diagram

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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 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

Image:SpiderEuler.jpg

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 of the sets from A through G, except for C, 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 [http://eprints.brighton.ac.uk/8159/ here]
Stapleton, G. and Howse, J. and Taylor, J. and Thompson, S. What can spider diagrams say? Proc. Diagrams, (2004) v. 168, pp. 169–219. Accessed on January 4, 2012 [https://web.archive.org/web/20120424023527/http://eprints.brighton.ac.uk/2864/1/D2K4SHTT.pdf here]
Stapleton, G. and Jamnik, M. and Masthoff, J. On the Readability of Diagrammatic Proofs Proc. Automated Reasoning Workshop, 2009. [https://web.archive.org/web/20171107002638/https://pdfs.semanticscholar.org/6ef5/3588293db667a11924d425a603ec9fdce75e.pdf PDF]

External links

[http://www.cs.kent.ac.uk/events/conf/2004/euler/eulerdiagrams.html Brighton and Kent University - Euler Diagrams]

Category:Diagrams

Category:Diagram algebras