2005
DOI: 10.1112/s1461157000000942
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Spider Diagrams

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 'spider diagrams'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 … Show more

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Cited by 95 publications
(127 citation statements)
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“…The implications of diagrammatic reasoning with an open universe is an interesting and open topic. Lastly, the use of absence could be incorporated into other Euler-diagram-based logics, such as spider diagrams [9], Euler/Venn diagrams [19], constraint diagrams [7] and concept diagrams [10].…”
Section: Discussionmentioning
confidence: 99%
“…The implications of diagrammatic reasoning with an open universe is an interesting and open topic. Lastly, the use of absence could be incorporated into other Euler-diagram-based logics, such as spider diagrams [9], Euler/Venn diagrams [19], constraint diagrams [7] and concept diagrams [10].…”
Section: Discussionmentioning
confidence: 99%
“…This section provides an overview of the syntax and semantics of spider diagrams of order, originally presented in [5] which in turn extends [11].…”
Section: Syntax and Semantics Of Spider Diagrams Of Ordermentioning
confidence: 99%
“…See, for example, [Stapleton 2005, Molina 2001] for surveys of various syntactic devices. Two Venn diagrams may be combined into another Venn diagram by accommodating the labels of circles and then by superposing the shaded regions, as illustrated in Fig.7.…”
Section: Linking Between Diagrams (For Disjunctive Information On Diamentioning
confidence: 99%
“…Venn-I and Venn-II systems of [Shin 1994]; Heterogeneous inference system of [Hammer 1994], Spider diagrams SD1 and SD2 of [Howse-Molina-Taylor 2000, Molina 2001], etc. For recent surveys, see [Stapleton 2005, Howse 2008.…”
Section: Linking Between Diagrams (For Disjunctive Information On Diamentioning
confidence: 99%