Visually Analyzing Universal Quantifiers in Photograph Captions

Universal quantifiers have been the subject of much work in symbolic and diagrammatic logic. However, little attention is paid to the question of how they can be visually grounded, that is, depicted in real images such as photographs. To investigate this question, we focus on universal quantifiers such as “all” and “every” used in an image captioning dataset and present a qualitative analysis of these expressions. The analysis revealed that although the use of universal quantifiers in image captions is rare, there are interesting patterns in their usage in terms of the semantics of visual representations. We distinguish two ways in which universal quantifiers are used in image captions. One is object-based quantification, which involves quantification over multiple discrete objects in a definite domain. The other is region-based quantification, where some property is ascribed to a salient continuous region in an image. We compare these two ways of visually representing universal quantification with two major representation systems studied in diagrammatic logic.