Journal of Logic, Language and Information

, Volume 26, Issue 2, pp 143–177 | Cite as

What Makes an Effective Representation of Information: A Formal Account of Observational Advantages



In order to effectively communicate information, the choice of representation is important. Ideally, a chosen representation will aid readers in making desired inferences. In this paper, we develop the theory of observation: what it means for one statement to be observable from another. Using observability, we give a formal characterization of the observational advantages of one representation of information over another. By considering observational advantages, people will be able to make better informed choices of representations of information. To demonstrate the benefit of observation and observational advantages, we apply these concepts to set theory and Euler diagrams. In particular, we can show that Euler diagrams have significant observational advantages over set theory. This formally justifies Larkin and Simon’s claim that “a diagram is (sometimes) worth ten thousand words”.


Observation Free rides Inference Euler diagrams Set theory 



We thank John Taylor and John Howse for their helpful comments on this work. Part of the research was undertaken whilst Gem Stapleton was at Doshisha University as a Visiting Scholar.

Supplementary material

10849_2017_9250_MOESM1_ESM.pdf (219 kb)
Supplementary material 1 (pdf 218 KB)


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Gem Stapleton
    • 1
  • Mateja Jamnik
    • 2
  • Atsushi Shimojima
    • 3
  1. 1.University of BrightonBrightonUK
  2. 2.University of CambridgeCambridgeUK
  3. 3.Doshisha UniversityKyotoJapan

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