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On the Completeness of Spider Diagrams Augmented with Constants

  • Gem Stapleton
  • John Howse
  • Simon Thompson
  • John Taylor
  • Peter Chapman
Part of the Studies in Universal Logic book series (SUL)

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.

Keywords

Spider diagrams Constants Soundness Completeness Monadic first-order logic Diagrammatic reasoning 

Mathematics Subject Classification (2010)

68R02 03B02 

Notes

Acknowledgement

This work is supported by the UK EPSRC grant “Defining Regular Languages with Diagrams” [EP/H012311/1].

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Gem Stapleton
    • 1
  • John Howse
    • 1
  • Simon Thompson
    • 2
  • John Taylor
    • 1
  • Peter Chapman
    • 1
  1. 1.Visual Modelling GroupUniversity of BrightonBrightonUK
  2. 2.School of ComputingUniversity of KentCanterburyUK

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