What Can Spider Diagrams Say?

Spider diagrams are a visual notation for expressing logical statements. In this paper we identify a well known fragment of first order predicate logic, that we call ESD, equivalent in expressive power to the spider diagram language. The language ESD 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 ESD that expresses the same information. For the more challenging converse we show 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.