Linear diagrams have recently been shown to be more effective than Euler diagrams when used for set-based rea- soning. However, unlike the growing corpus of knowledge about formal aspects of Euler and Venn diagrams, there has been no formalisation of linear diagrams. To fill this knowl- edge gap, we present and formalise Point and Line (PaL) di- agrams, an extension of simple linear diagrams containing points, thus providing a formal foundation for an effective visual language. We prove that PaL diagrams are exactly as expressive as monadic first-order logic with equality, gain- ing, as a corollary, an equivalence with the Euler diagram extension called spider diagrams. The method of proof pro- vides translations between PaL diagrams and sentences of monadic first-order logic.
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- Line diagrams
- First-order logic
Chapman, P., Stapleton, G., & Rodgers, P. (2014). PaL Diagrams: a linear diagram-based visual language. Journal of Visual Languages and Computing, 25(6), 945-954. https://doi.org/10.1016/j.jvlc.2014.10.022