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 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

∧

,

∨

,

¬

{\displaystyle \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

∧

B

{\displaystyle A\land B}

B

∧

C

{\displaystyle B\land C}

F

∧

E

{\displaystyle F\land E}

G

∧

F

{\displaystyle 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

∧

E

)

∨

(

G

)

∨

(

D

)

{\displaystyle (F\land E)\lor (G)\lor (D)}

Blue spider:

(

A

)

∨

(

C

∧

B

)

∨

(

F

)

{\displaystyle (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.