Do monkeys like elephants or do elephants watch monkeys? An empirical study into the default reading of constraint diagrams

Constraint diagrams complement the Unified Modeling Language that is used in the development of software systems. They generalize Venn and Euler diagrams, and include facilities for quantification and navigation of relations. Difficulties such as ordering quantifiers cause constraint diagrams to have more than one possible meaning. Fish et al. have extended the constraint diagram notation, augmenting it with a reading tree which provides a unique semantics. However, this involves extracting extra information about the reading order from the diagram creator. Progress has been made towards a default reading, which extracts this information implicitly from the diagram. In this paper, we investigate how humans read ambiguous constraint diagrams intuitively, without any instructions on the reading order. We test several principles which could be used in a default reading. We conclude that although some of these principles have significant effects, they also may conflict. Either an explicit reading tree or a taught method of reading a diagram which may conflict with some people’s intuition is necessary.