User-comprehension of Euler diagrams

Andrew Fish, Babak Khazaei, Chris Roast

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)340-354
Number of pages15
JournalJournal of Visual Languages and Computing
Issue number5
Publication statusPublished - 1 Oct 2011


  • Usability of diagrams and mathematical notation
  • Comprehension of diagrams
  • Empirical study
  • Wellformed and non-wellformed Euler diagrams


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