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Spider diagrams

By John Howse, Gem Stapleton and John Taylor

Abstract

The use of diagrams in mathematics has traditionally been restricted to guiding intuition and communication. With rare exceptions such as Peirce's α and β systems, purely diagrammatic formal reasoning has not been in the mathematician's or logician's toolkit. This paper develops a purely diagrammatic reasoning system of ‘spiderdiagrams' that builds on Euler, Venn and Peirce diagrams.The system is known to be expressively equivalent to first-order monadic logic with equality. Two levels of diagrammatic syntax have been developed: an ‘abstract' syntax that captures the structure of diagrams,and a ‘concrete' syntax that captures topological properties of drawn diagrams. A number of simple diagrammatic transformation rules are given, and the resulting reasoning system is shown to be sound and complete

Topics: G000 Computing and Mathematical Sciences
Publisher: Cambridge University Press
Year: 2005
DOI identifier: 10.1112/S1461157000000942
OAI identifier: oai:eprints.brighton.ac.uk:8159
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