User-comprehension of Euler diagrams

Euler diagrams are a diagrammatic system for representing and reasoning with set theoretic statements. Syntactic constraints called wellformedness conditions (WFCs) are often imposed with the intention of reducing comprehension errors, but there is little supporting empirical evidence that they have the desired effect. We report on experiments which support the theory that the WFCs are generally beneficial for novice user comprehension, but we discover that violating some individual WFCs, such as concurrency, can be beneficial. Furthermore, we examine a prioritisation of the WFCs, derived from the user comprehension results, which could be used to prioritise theoretical work on generation problems or to assist in the provision of a choice of a diagram to display to users, for instance. We have used similar materials to our previous ‘preference study’ for cross comparison purposes. This accumulation of work has motivated the development of a model of the user comprehension with the aim of more closely linking theoretical and empirical works examining effective notation design, general approaches to displaying notations and interacting with notations.

Research highlights
► First empirical study on this topic.
► Effect on comprehension of violation of Euler diagram wellformedness conditions.
► Impositions of WFCs are generally beneficial for novice user comprehension.
► Individual violation (e.g. of complete concurrency of curves) can be beneficial.
► Proposed prioritisation of the WFC and a model of user comprehension.