Jin Yuelin’s Simplification of Venn Diagrams

Xinwen Liu, Ahti Veikko Pietarinen*

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review


Chinese logician and philosopher Jin Yuelin published in 1935 a textbook Logic (in Chinese) in which he proposed proving the distributive laws by a slightly non-standard version of Venn diagrams. In Jin Yuelin’s modification some segments of the circles are marked with dashed instead of continuous lines, namely those that following the meet and join operations encircle the regions outside of the meet regions, as well as those that encircle the regions inside of the join regions. Hence the validity of distribution of meets over joins in the first distributive law and joins over meets in the second is observed by the sameness of the diagrams with exactly the same dashed and continuous line segments. This slight modification removes the need for shading empty regions and liberates one from using the cross mark “x” or some other ‘non-visuals’ for existence while freeing shading for some other uses (as e.g. opined by Venn and Peirce) and reducing clutter. In addition to such implications to the theory of Venn diagrams, we expose this little-known detail from the history of Venn diagrams and assess the factors that contributed to its discovery, such as whether Jin Yuelin decided to apply the dashed line following his reading of Peirce’s broken-cut notations.

Original languageEnglish
Title of host publicationDiagrammatic Representation and Inference
Subtitle of host publication12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings
EditorsAmrita Basu, Gem Stapleton, Sven Linker, Catherine Legg, Emmanuel Manalo, Petrucio Viana
PublisherSpringer Cham
Number of pages4
ISBN (Electronic)9783030860622
ISBN (Print)9783030860615
Publication statusPublished - 3 Sept 2021
Event12th International Conference on the Theory and Application of Diagrams, Diagrams 2021 - Virtual, Online
Duration: 28 Sept 202130 Sept 2021

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349
NameLecture Notes in Artificial Intelligence
NameDiagrams: International Conference on Theory and Application of Diagrams


Conference12th International Conference on the Theory and Application of Diagrams, Diagrams 2021
CityVirtual, Online
Internet address

Scopus Subject Areas

  • Theoretical Computer Science
  • Computer Science(all)

User-Defined Keywords

  • Dashed circles
  • Distributivity
  • Jin Yuelin
  • Peirce
  • Venn diagrams


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