A compositional semantics for Venn diagrams

This paper examines Venn diagrams as a case study of visual representation. Venn diagrams have a clear formal structure and clearly defined correctness conditions. The question for this paper is whether these diagrams have a recursive syntax and corresponding compositional semantics by analogy with those developed for formal or natural languages. Existing research pointedly fails to offer a compositional semantics for Venn diagrams. This might suggest a fundamental cleavage between linguistic representation and the kind of visual representation exhibited by diagrams. Or, it might indicate a case of representation that recalcitrantly resists compositional analysis. This paper presents two approaches to the syntax of Venn diagrams: a region-first approach and a cell-first approach. It then develops a compositional semantics for each approach. The paper therefore helps to locate the similarities and differences more precisely between linguistic representation and the kind of representation exhibited by Venn diagrams. The two approaches to the syntax and semantics for Venn diagrams also suggest new avenues for interpreting other forms of visual representation.