The Expressiveness of Spider Diagrams Augmented with Constants

Authors:
Gem Stapleton;John Howse;John Taylor;Simon Thompson
Affiliations:
University of Brighton, UK;University of Brighton, UK;University of Brighton, UK;University of Kent, Canterbury, UK
Venue:
VLHCC '04 Proceedings of the 2004 IEEE Symposium on Visual Languages - Human Centric Computing
Year:
2004

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The expressiveness of spider diagrams augmented with constants

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Abstract

Spider diagrams are a visual language for expressing logical statements. Spiders represent the existence of elements and contours denote sets. Several sound and complete spider diagram systems have been developed and it is known that the spider diagram language is equivalent in expressive power to monadic first order logic with equality. However, these sound and complete spider diagram systems do not contain syntactic elements analogous to constants in first order predicate logic. We extend the spider diagram language to include constant spiders which represent specific individuals and give formal semantics for the extended diagram language. We then prove that this extended system is equivalent in expressive power to the language of spider diagrams without constants.