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What is a Logical Diagram? Read chapter Read first chapter

2013 | OriginalPaper | Chapter

On the Completeness of Spider Diagrams Augmented with Constants

Authors : Gem Stapleton, John Howse, Simon Thompson, John Taylor, Peter Chapman

Published in: Visual Reasoning with Diagrams

Publisher: Springer Basel

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Abstract

Diagrammatic reasoning can be described formally by a number of diagrammatic logics; spider diagrams are one of these, and are used for expressing logical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that represent specific individuals. We give a formal syntax and semantics for the extended diagram language before introducing a collection of reasoning rules encapsulating logical equivalence and logical consequence. We prove that the resulting logic is sound, complete and decidable.

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previous chapter Diagrammatic Reasoning with Classes and Relationships
next chapter A Practice-Based Approach to Diagrams
Footnotes
1
Since all constructs discussed here are abstract, we will use the terminology ‘zone’ rather than ‘abstract zone’ throughout.
 
2
However, for any diagram that incorporated such ties it is possible to define a semantically equivalent diagram that does not contain such ties. This is not the case for ties between constant spiders. It is straightforward to extend the work in this paper to the case where these additional types of tie are permitted.
 
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Metadata
Title
On the Completeness of Spider Diagrams Augmented with Constants
Authors
Gem Stapleton
John Howse
Simon Thompson
John Taylor
Peter Chapman
Copyright Year
2013
Publisher
Springer Basel
Book
Visual Reasoning with Diagrams

Print ISBN: 978-3-0348-0599-5

Electronic ISBN: 978-3-0348-0600-8

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-0348-0600-8_7

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