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

    1 Citation (Scopus)

    Abstract

    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
    Pages260-263
    Number of pages4
    Edition1st
    ISBN (Electronic)9783030860622
    ISBN (Print)9783030860615
    DOIs
    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
    https://link.springer.com/book/10.1007/978-3-030-86062-2

    Publication series

    NameLecture Notes in Computer Science
    Volume12909
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349
    NameLecture Notes in Artificial Intelligence
    NameDiagrams: International Conference on Theory and Application of Diagrams

    Conference

    Conference12th International Conference on the Theory and Application of Diagrams, Diagrams 2021
    CityVirtual, Online
    Period28/09/2130/09/21
    Internet address

    Scopus Subject Areas

    • Theoretical Computer Science
    • General Computer Science

    User-Defined Keywords

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

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