In mathematics, a unitary spider diagram adds existential points to an Euler or a

Venn diagram A Venn diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are used to teach elementary set theory, and to illustrate simple set relationships ...

. 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 Spiders ( order Araneae) are air-breathing arthropods that have eight legs, chelicerae with fangs generally able to inject venom, and spinnerets that extrude silk. They are the largest order of arachnids and rank seventh in total species ...

. Joined points represent an "or" condition, also known as a

logical disjunction In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor ...

. 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

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 In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range. Overview The doma ...

defined by this

Euler diagram An Euler diagram (, ) is a diagrammatic means of representing sets and their relationships. They are particularly useful for explaining complex hierarchies and overlapping definitions. They are similar to another set diagramming technique, Ven ...

, 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 set In mathematics, a singleton, also known as a unit set or one-point set, is a set with exactly one element. For example, the set \ is a singleton whose single element is 0. Properties Within the framework of Zermelo–Fraenkel set theory, the ...

s 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. Accessed on January 8, 201
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, 201
here
* Stapleton, G. and Jamnik, M. and Masthoff, J. ''On the Readability of Diagrammatic Proofs'' Proc. Automated Reasoning Workshop, 2009
PDF

External links

{{commons category, Spider diagrams

Diagrams Diagram algebras