Abstract
The ability of diagrams to convey information effectively in part comes from their ability to make facts explicit that would otherwise need to be inferred. This type of advantage has often been referred to as a free ride and was deemed to occur only when a diagram was obtained by translating a symbolic representation of information. Recent work generalised free rides to the idea of an observational advantage, where the existence of such a translation is not required. Roughly speaking, it has been shown that Euler diagrams without existential import are observationally complete as compared to symbolic set theory. In this paper, we explore to what extent Euler diagrams with existential import are observationally complete with respect to set-theoretic sentences. We show that existential import significantly limits the cases when observational completeness arises, due to the potential for overspecificity.
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Notes
- 1.
In Euler diagrams without existential import, zones can represent empty sets. By contrast, under existential import all zones in the diagram represent non-empty sets [7]. Peirce denotes non-emptiness of a set with \(\otimes \)-sequences [12] (also used by Shin [15] and further developed by Choudhury and Chakraborty [4]). Other notations use graphs to denote elements in sets [6, 8, 9].
- 2.
It is possible to define observability for other types of diagrams and statements too.
- 3.
It is straightforward, yet lengthy, to define a translation from regions to set-expressions; due to space constraints, we refer the reader to [16].
References
Baigelenov, A., Saenz, M., Hung, Y.H., Parsons, P.: Toward an understanding of observational advantages in information visualization. In: IEEE Conference on Information Visualization, Poster Abstracts (2017)
Barwise, J., Etchemendy, J.: Hyperproof. CSLI Press, Stanford (1994)
Chatti, S., Schang, F.: The cube, the square and the problem of existential import. Hist. Philos. Logic 34(2), 101–132 (2013)
Choudhury, L., Chakraborty, M.K.: On extending venn diagram by augmenting names of individuals. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds.) Diagrams 2004. LNCS (LNAI), vol. 2980, pp. 142–146. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-25931-2_14
Dretske, F.: Seeing and Knowing. Routledge & Kegan Paul, London (1969)
Gil, J., Howse, J., Kent, S.: Formalising spider diagrams. In: IEEE Symposium on Visual Languages, pp. 130–137. IEEE (1999)
Hammer, E., Shin, S.J.: Euler’s visual logic. Hist. Philos. Logic 19, 1–29 (1998)
Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS J. Comput. Math. 8, 145–194 (2005)
Kent, S.: Constraint diagrams: visualizing invariants in object oriented models. In: Proceedings of OOPSLA 1997, pp. 327–341. ACM Press, October 1997
Mineshima, K., Okada, M., Takemura, R.: A diagrammatic inference system with Euler circles. J. Logic Lang. Inform. 21(3), 365–391 (2012)
Moktefi, A., Pietarinen, A.V.: On the diagrammatic representation of existenial statements with Venn diagrams. J. Logic Lang. Inform. 24(4), 361–374 (2015)
Peirce, C.: Collected Papers, vol. 4. Harvard University Press, Cambridge (1933)
Sato, Y., Mineshima, K., Takemura, R.: The efficacy of Euler and Venn diagrams in deductive reasoning: empirical findings. In: Goel, A.K., Jamnik, M., Narayanan, N.H. (eds.) Diagrams 2010. LNCS (LNAI), vol. 6170, pp. 6–22. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14600-8_6
Shimojima, A.: Semantic Properties of Diagrams and Their Cognitive Potentials. CSLI, Stanford (2015)
Shin, S.J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)
Stapleton, G., Jamnik, M., Shimojima, A.: What makes an effective representation of information: a formal account of observational advantages. J. Logic Lang. Inform. 26(2), 143–177 (2017)
Stenning, K., Oberlander, J.: A cognitive theory of graphical and linguistic reasoning: logic and implementation. Cogn. Sci. 19(1), 97–140 (1995)
Swoboda, N., Allwein, G.: Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference. J. Softw. Syst. Model. 3(2), 136–149 (2004)
Acknowledgements
Stapleton and Jamnik were funded by a Leverhulme Trust Research Project Grant (RPG- 2016-082) for the project entitled Accessible Reasoning with Diagrams.
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Stapleton, G., Shimojima, A., Jamnik, M. (2018). The Observational Advantages of Euler Diagrams with Existential Import. In: Chapman, P., Stapleton, G., Moktefi, A., Perez-Kriz, S., Bellucci, F. (eds) Diagrammatic Representation and Inference. Diagrams 2018. Lecture Notes in Computer Science(), vol 10871. Springer, Cham. https://doi.org/10.1007/978-3-319-91376-6_29
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