Spider diagrams

HOWSE, JOHN, STAPLETON, GEM and TAYLOR, JOHN (2005) Spider diagrams LMS Journal of Computation and Mathematics, 8 . pp. 145-194. ISSN 1461-1570

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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.

Item Type:Journal article
Additional Information:© 2005 London Mathematical Society
Subjects:G000 Computing and Mathematical Sciences
DOI (a stable link to the resource):10.1112/S1461157000000942
Faculties:Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Visual Modelling
ID Code:8159
Deposited By:Converis
Deposited On:04 Feb 2011 11:11
Last Modified:02 Jul 2013 04:02

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