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The expressiveness of spider diagrams

By Gem Stapleton, John Howse, John Taylor and Simon Thompson

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

Topics: G000 Computing and Mathematical Sciences
Publisher: Oxford University Press
Year: 2004
DOI identifier: 10.1093/logcom
OAI identifier: oai:eprints.brighton.ac.uk:8158
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