The Expressiveness of Spider Diagrams

  • Authors:

  • Gem Stapleton;John Howse;John Taylor;Simon Thompson

  • Affiliations:

  • Visual Modelling Group, School of Computing, Mathematical and Information Sciences, University of Brighton, Brighton, BN2 4GJ, UK. E-mail: g.e.stapleton@brighton.ac.uk, john.howse@brighton.ac.uk, ...;Visual Modelling Group, School of Computing, Mathematical and Information Sciences, University of Brighton, Brighton, BN2 4GJ, UK. E-mail: g.e.stapleton@brighton.ac.uk, john.howse@brighton.ac.uk, ...;Visual Modelling Group, School of Computing, Mathematical and Information Sciences, University of Brighton, Brighton, BN2 4GJ, UK. E-mail: g.e.stapleton@brighton.ac.uk, john.howse@brighton.ac.uk, ...;University of Kent, Canterbury, Kent, CT2 7NF, UK. E-mail: s.j.thompson@kent.ac.uk

  • Venue:
  • Journal of Logic and Computation
  • Year:
  • 2004

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Abstract

Spider diagrams are a visual language for expressing logical statements. In this paper we identify a well-known fragment of first-order predicate logic that we call MFOL=, equivalent in expressive power to the spider diagram language. The language MFOL= is monadic and includes equality but has no constants or function symbols. To show this equivalence, in one direction, for each diagram we construct a sentence in MFOL= that expresses the same information. For the more challenging converse we prove that there exists a finite set of models for a sentence S that can be used to classify all the models for S. Using these classifying models we show that there is a diagram expressing the same information as S.