Reasoning with Diagrams: Observation, Inference and Overspecificity

The ability of diagrams to convey information effectivelycomes, in part, from their ability to make facts explicit that would otherwise need to be inferred. This type of advantagehas often been referred to as a free ride and was deemed to occur only when a diagram was obtained by translating asymbolic representation of information. Recent work generalised free rides, introducing the idea of an observational advantage, where the existence of such a translation is not required. In this paper, I will provide an overview of the theory of observation. It has been shown that Euler diagrams without existential import have significant observational advantages over set theory: they are observationallycomplete. I will then explore to what extent Euler diagrams with existential import are observationally complete with respect to set-theoretic sentences. In particular, has been shown that existential import significantly limits the cases when observational completeness arises, due to the potentialfor overspecificity. These two results formally support Larkin and Simon's claim that "a diagram is (sometimes)worth ten thousand words". The work in this invited paperis derived from previously published results as cited in the text.