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.

In the image shown, the following conjunctions are apparent from the Euler diagram.

${\displaystyle A\land B}$

${\displaystyle B\land C}$

${\displaystyle F\land E}$

${\displaystyle G\land F}$

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: ${\displaystyle (F\land E)\lor (G)\lor (D)}$
• Blue spider: ${\displaystyle (A)\lor (C\land B)\lor (F)}$

• 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, pp. 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

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