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Journal of Logic and Computation 2004 14(6):857-880; doi:10.1093/logcom/14.6.857
© 2004 by Oxford University Press
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The Expressiveness of Spider Diagrams

Gem Stapleton1, John Howse1, John Taylor1 and Simon Thompson2

1 Visual Modelling Group, School of Computing, Mathematical and Information Sciences, University of Brighton, Brighton, BN2 4GJ, UK. E-mail: g.e.stapleton{at}brighton.ac.uk, john.howse{at}brighton.ac.uk, john.taylor{at}brighton.ac.uk, 2 University of Kent, Canterbury, Kent, CT2 7NF, UK. E-mail: s.j.thompson{at}kent.ac.uk

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.

Keywords: Spider diagrams, expressiveness, monadic logic, model theory

Received 15 March 2004.


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