Skip to main content
Log in

The Semiotics of Spider Diagrams

  • Published:
Logica Universalis Aims and scope Submit manuscript

Abstract

Spider diagrams are based on Euler and Venn/Peirce diagrams, forming a system which is as expressive as monadic first order logic with equality. Rather than being primarily intended for logicians, spider diagrams were developed at the end of the 1990s in the context of visual modelling and software specification. We examine the original goals of the designers, the ways in which the notation has evolved and its connection with the philosophical origins of the logical diagrams of Euler, Venn and Peirce on which spider diagrams are based. Using Peirce’s concepts and classification of signs, we analyse the ways in which different sign types are exploited in the notation. Our hope is that this analysis may be of interest beyond those readers particularly interested in spider diagrams, and act as a case study in deconstructing a simple visual logic. Along the way, we discuss the need for a deeper semiotic engagement in visual modelling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Allwein, G., Barwise, J. (eds.): Logical Reasoning with Diagrams (Studies in Logic and Computation), 1st edn. Oxford University Press, Oxford (1996)

    Google Scholar 

  2. Alqadah, M., Stapleton, G., Howse, J., Chapman, P.: Evaluating the impact of clutter in Euler diagrams. In: Dwyer, T., Purchase, H., Delaney, A. (eds.), Diagrammatic Representation and Inference, vol 8578 of Lecture Notes in Computer Science, pp. 108–122. Springer (2014)

  3. Atkin, A.: Peirce (The Routledge Philosophers). Routledge, London (2015)

    Google Scholar 

  4. Barwise, J., Etchemendy, J.: Heterogeneous Logic, pp. 179–200. Oxford University Press Inc., New York (1996)

    Google Scholar 

  5. Barwise, J., Etchemendy, J.: Language Proof and Logic. CSLI, Stanford (1999)

    MATH  Google Scholar 

  6. Bellucci, F., Pietarinen, A.V.: Existential graphs as an instrument of logical analysis: Part I. Alpha. Rev. Symbol. Logic FirstView 9(2), 209–237 (2016)

  7. Blake, A., Stapleton, G., Rodgers, P., Howse, J.: The impact of topological and graphical choices on the perception of euler diagrams. Information Sciences 330, 455–482 (2016)

    Article  Google Scholar 

  8. Burton, J., Stapleton, G., Howse, J.: Completeness strategies for visual logics. In: 7th International Conference on the Theory and Application of Diagrams, (2012)

  9. Chen, P.P.: The entity-relationship model—toward a unified view of data. ACM Trans. Database Syst. 1(1), 9–36 (1976)

    Article  MathSciNet  Google Scholar 

  10. Choudhury, L., Chakraborty, M.K.: On extending Venn diagrams by augmenting names of individuals. In: Proceedings of 3rd International Conference on the Theory and Application of Diagrams, volume 2980 of LNAI, pp. 142–146. Springer (2004)

  11. Delaney A., Taylor J., Thompson S.: Spider diagrams of order and a hierarchy of star-free regular languages. In: Stapleton G., Howse J., Lee J. (eds) Diagrammatic representation and inference. Diagrams 2008. LNAI 5223, pp 172–187, Springer (2008)

  12. Bertin, J.: Semiology of graphics: diagrams, networks, maps. University of Wisconsin Press, (1983)

  13. Euler, L.: Lettres a une Princesse d’Allemagne sur divers sujets de physique et de philosophie. Letters 2, 102–108 (1775)

    Google Scholar 

  14. Fish, A., Flower, J., Howse, J.: The semantics of augmented constraint diagrams. J. Vis. Lang. Comput. 16, 541–573 (2005)

    Article  Google Scholar 

  15. Gil, J., Howse, J., Kent, S.: Formalizing spider diagrams. In: Proceedings of IEEE Symposium on Visual Languages (VL99), Tokyo, pp. 130–137 (1999)

  16. Gurr, C., Tourlas, K.: Towards the principled design of software engineering diagrams. In: Proceedings of 22nd International Conference on Software Engineering, pp. 509–518. ACM Press (2000)

  17. Gurr, C.: Effective diagrammatic communication: syntactic, semantic and pragmatic issues. J. Vis. Lang. Comput. 10(4), 317–342 (1999)

    Article  Google Scholar 

  18. Hammer, E., Shin, S.J.: Euler’s visual logic. Hist Philos Logic 19, 1–29 (1998)

  19. Hammer, E.: Logic and Visual Information. Centre for the Study of Language and Information (CSLI) publications, Stanford, CA. (1995)

  20. Harel, D.: Statecharts: a visual formalism for complex systems. Sci. Comput. Program. 8(3), 231–274 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hitchman, S.: The details of conceptual modelling notations are important—a comparison of relationship normative language. Commun. Assoc. Inf. Syst. 9(1), Article 10 (2002)

  22. Howse, J., Molina, F., Shin, S.J., Taylor, J.: On diagram tokens and types. In: Proceedings of 2nd International Conference on the Theory and Application of Diagrams, Georgia, USA, pp. 146–160. Springer (2002)

  23. Howse, J., Molina, F., Taylor, J., Kent, S.: Reasoning with spider diagrams. In: Proceedings of IEEE Symposium on Visual Languages (VL99), Tokyo, pp. 138–147 (1999)

  24. Howse, J., Molina, F., Taylor, J.: SD2: a sound and complete diagrammatic reasoning system. In: Proceedings VL 2000: IEEE Symposium on Visual Languages, Seattle, USA, pp. 127–136 (2000)

  25. Howse, J., Stapleton, G., Taylor, J.: Spider diagrams. LMS J. Comput. Math. 8, 145–194 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  26. Jansen, D.N., Hermanns, H., Katoen, J.: UML 2003-the unified modeling language. In: UML 2003-The Unified Modeling Language, pp. 76–91. Springer (2003)

  27. John, C., Fish, A., Howse, J., Taylor, J.: Exploring the notion of clutter in Euler diagrams. In 4th International Conference on the Theory and Application of Diagrams, Stanford, USA, pp. 267–282. Springer (2006)

  28. Kent, S.: Constraint diagrams: visualizing invariants in object oriented modelling. In: Proceedings of OOPSLA97, pp. 327–341. ACM Press (1997)

  29. Legg, C.: What is a logical diagram? In: Moktefi, A., Shin, S. (eds.) Visual Reasoning with Diagrams. Studies in Universal Logic, pp. 1–18. Springer, Basel (2013)

    Chapter  Google Scholar 

  30. Moktefi, A.: Is Euler’s circle a symbol or an icon? Sign Syst. Stud. 43(4), 597 (2015)

    Article  MathSciNet  Google Scholar 

  31. Moktefi, A., Shin, S.-J.: A history of logic diagrams. In: Gabbay, D.M., Pelletier, F.J., Woods, J. (eds.) Handbook of the History of Logic, vol. 11, pp. 611–682. Elsevier, New York (2012)

    Google Scholar 

  32. Oliver, I., Howse, J., Stapleton, G.: Protecting privacy: towards a visual framework for handling end-user data. In: VL/HCC’13, pp. 67–74 (2013)

  33. Peirce, C.S.: Collected Papers, vol. 4. Harvard University Press, Cambridge (1933)

    MATH  Google Scholar 

  34. Pietarinen, A.: Extensions of euler diagrams in peirce’s four manuscripts on logical graphs. In: Jamnik, M., Uesaka, Y., Elzer Schwartz, S. (eds.) Diagrammatic Representation and Inference: 9th International Conference. Diagrams 2016, Philadelphia, PA, USA, August 7–10, 2016, Proceedings, pp. 139–154. Springer, Cham (2016)

  35. Roberts, D.: The Existential Graphs of Charles S. Peirce (Approaches to Semiotics), 1st edn. De Gruyter Mouton, Berlin (1973)

    Google Scholar 

  36. Sato, Y., Mineshima, K., Takemura, R.: Interpreting logic diagrams: a comparison of two formulations of diagrammatic representations. In: Proceedings of the 33rd Annual Meeting of the Cognitive Science Society, CogSci 2011, Boston, USA, 2011, (2011)

  37. Shimojima, A.: Inferential and expressive capacities of graphical representations: Survey and some generalizations. In: Proceedings of 3rd International Conference on the Theory and Application of Diagrams, volume 2980 of LNAI, pp. 18–21, Cambridge, UK. Springer (2004)

  38. Shimojima, A.: Logical reasoning with diagrams. In: Allwein, Gerard, Barwise, Jon (eds.) Logical Reasoning with Diagrams, chapter Operational Constraints in Diagrammatic Reasoning, pp. 27–48. Oxford University Press Inc, New York (1996)

    Google Scholar 

  39. Shin, S.J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)

    MATH  Google Scholar 

  40. Sowa, J.F.: Conceptual Structures: Information Processing in Mind and Machine. Systems Programming Series. Addison-Wesley, Boston (1983)

    Google Scholar 

  41. Stapleton, G., Delaney, A.: Towards overcoming deficiencies in constraint diagrams. In: Symposium on Visual Languages and Human-Centric Computing, pp. 33–40 (2007)

  42. Howse J., Stapleton G., Taylor K., Chapman P.: Visualizing Ontologies: A Case Study. In: Aroyo L. et al. (eds) The Semantic Web – ISWC 2011. ISWC 2011. Lecture Notes in Computer Science, vol 7031. Springer, Berlin, Heidelberg (2011)

  43. Stapleton, G., Howse, J., Taylor, J.: A constraint diagram reasoning system. In: Proceedings of International Conference on Visual Languages and Computing, pp. 263–270. Knowledge Systems Insitute (2003)

  44. Stapleton, G., Taylor, J., Howse, J., Thompson, S.: The expressiveness of spider diagrams augmented with constants. J. Vis. Lang. Comput. 20(1), 30–49, (2009)

  45. Stjernfelt, F.: On operational and optimal iconicity in Peirce’s diagrammatology. Semiotica 2011(186), 395–419 (2011)

  46. Stjernfelt, F.: Diagrams as a centrepiece of a Peircean epistemology. Trans. Charles S Peirce Soc. 36(3), 357–384 (2000)

    Google Scholar 

  47. Stjernfelt, F.: Two iconicity notions in peirce’s diagrammatology. In: Schärfe, H., Hitzler, P., Øhrstrøm, P. (eds.) Conceptual Structures: Inspiration and Application: 14th International Conference on Conceptual Structures. ICCS 2006, pp. 70–86. Springer, Berlin (2006)

    Google Scholar 

  48. Stjernfelt, F.: Dicisigns. Synthese 192(4), 1019–1054 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  49. Venn, J.: On the Diagrammatic and Mechanical Representation of Propositions and Reasonings. Philos. Mag. 10(59), 1–18 (1880)

  50. Zeman, J.: A system of implicit quantification. J. Symb. Logic 32, 480–504 (1968)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John Howse.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Burton, J., Howse, J. The Semiotics of Spider Diagrams. Log. Univers. 11, 177–204 (2017). https://doi.org/10.1007/s11787-017-0167-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11787-017-0167-2

Keywords

Mathematics Subject Classification

Navigation