Skip to main content
SpringerLink
Log in

Significance in Marlo Diagrams Versus Thoroughness of Venn Diagrams

  • Conference paper
  • First Online:
Intelligent Computing (SAI 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 506))

Included in the following conference series:

  • 771 Accesses

Abstract

Logical diagrams allow expressing intuitively the exact analogy that exists between the relations of concepts and those of spatial figures. Undoubtedly, among the logical diagrams, those created by Venn stand out. These diagrams form a complete logical system with a well-defined syntax, equivalent to the monadic logic of the first order. However, Venn diagrams have the disadvantage that they need to explicitly and comprehensively show all the combinations that make up the universe of discourse, including empty classes. This requirement considerably reduces clarity and its usefulness as the number of letters increases. By contrast, Marlo diagram, quantifying the predicate and without giving up the functional dichotomy “subject-predicate”, overcomes this difficulty and can communicate the same information with rigor and precision, but more economically, handling only relevant information. In this way, it is possible to maintain a greater correspondence between the formal notation, the linguistic processes that lead us from the premises to the conclusion, and the graphic representation of each of the reasoning steps that underlie the inference. After many years of efforts to make our diagrams simple and intuitive tools for the didactics of logic, we present here a more detailed analysis of some of its operations that could be useful to investigate the constitutive processes of reasoning involved in First-order logic.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abeles, F.F.: Lewis Carroll’s visual logic. Hist. Philos. Log. 28(1), 1–17 (2007). https://doi.org/10.1080/01445340600704481

    Article  MathSciNet  MATH  Google Scholar 

  2. Alemany, F.S.: Hacia la lógica plástica: emergencia de la lógica del razonamiento visual. Contextos 16(31–32), 281–296 (1998)

    Google Scholar 

  3. Allwein, G., Barwise, J.: Logical Reasoning with Diagrams. Oxford University Press, New York (1996)

    Book  Google Scholar 

  4. Aznar, M.B.L.: Adiós a bArbArA y Venn. Lógica de predicados en el diagrama. Paideia Revista de Filosofía y didáctica filosófica 35(102), 35–52 (2015)

    Google Scholar 

  5. Aznar, M.B.L.: Visual reasoning in the Marlo diagram. In: Sato, Y., Shams, Z. (eds.) SetVR@ Diagrams, vol. 2116. Ceurws.org (2018). http://ceur-ws.org/Vol-2116

  6. Aznar, M.B.L.: Visual reasoning in the Marlo diagram (2018). [video file]. https://www.youtube.com/watch?v=ivEZ4Pfr6tQ&t=7s

  7. Aznar, M.B.L.: The Marlo diagram in the classroom. In: Pietarinen, A.-V., Chapman, P., Bosveld-de Smet, L., Giardino, V., Corter, J., Linker, S. (eds.) Diagrams 2020. LNCS (LNAI), vol. 12169, pp. 490–493. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-54249-8_41

    Chapter  Google Scholar 

  8. Aznar, M.B.L.: Syllogisms with intermediate quantifiers solved in Marlo logic diagrams. In: Pietarinen, A.-V., Chapman, P., Bosveld-de Smet, L., Giardino, V., Corter, J., Linker, S. (eds.) Diagrams 2020. LNCS (LNAI), vol. 12169, pp. 473–476. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-54249-8_37

    Chapter  Google Scholar 

  9. Aznar, M.B.L: Diagramas lógicos de Marlo para el razonamiento visual y heterogéneo: válidos en lógica matemática y aristotélica. Unpublished doctoral dissertation, University of Huelva, Spain (2020)

    Google Scholar 

  10. Bocheński, I.M.: A History of Formal Logic. University of Notre Dame Press, Notre Dame (1961)

    MATH  Google Scholar 

  11. Boole, G.: An Investigation of the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities. Dover, New York (1854)

    Book  Google Scholar 

  12. Carroll, L.: The Game of Logic. Macmillan, London (1886)

    Google Scholar 

  13. Castro-Manzano, J.: Remarks on the idea of non-monotonic (diagrammatic) inference. Open Insight 8(14), 243–263 (2017)

    Article  Google Scholar 

  14. Chen, H., Boutros, P.C.: Venn diagram: a package for the generation of highly customizable Venn and Euler diagrams in R. BMC Bioinform. 12(1), 35 (2011). https://doi.org/10.1186/1471-2105-12-35

    Article  Google Scholar 

  15. Címbora Acosta, G.: Lógica en el Diagrama de Marlo. Tratando de hacer evidente la certeza. In: Campillo, A., Manzanero, D. (eds.) Actas II Congreso Internacional de la Red española de Filosofía, pp. 41–55. REF, Madrid (2017). http://redfilosofia.es/congreso/wp-content/uploads/sites/4/2017/07/7.5.pdf

  16. Gardner, M.: Logic Machines and Diagrams. McGraw-Hill, New York/Toronto/London (1958)

    MATH  Google Scholar 

  17. Giardino, V.: Diagrammatic reasoning in mathematics. In: Magnani, L., Bertolotti, T. (eds.) Springer Handbook of Model-Based Science. SH, pp. 499–522. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-30526-4_22

    Chapter  Google Scholar 

  18. Hamilton, W.: Lectures on Metaphysics and Logic, vol. IV. William Blackwood and Sons, Edinburgh/London (1860)

    Google Scholar 

  19. Hammer, E., Shin, S.: Euler’s visual logic. Hist. Philos. Log. 19(1), 1–29 (1998). https://doi.org/10.1080/01445349808837293

    Article  MathSciNet  MATH  Google Scholar 

  20. Jevons, W.: Pure Logic or the Logic of Quality. Stanford, London (1864)

    Google Scholar 

  21. Johnson-Laird, P.: Peirce, logic diagrams, and the elementary operations of reasoning. Think. Reason. 8(1), 69–95 (2002). https://doi.org/10.1080/13546780143000099

    Article  Google Scholar 

  22. Legris, J.: Visualizar y manipular: sobre el razonamiento diagramático y la naturaleza de la deducción. In: Lassalle Cassanave, A., Thomas Sautter, F. (eds.) Visualização nas Ciências Formais, pp. 89–103. College Publications, London (2012)

    Google Scholar 

  23. Macbeth, D.: Realizing Reason: A Narrative of Truth and Knowing. Oxford University Press, Oxford (2014). https://doi.org/10.1093/acprof:oso/9780198704751.001.0001

  24. Marlo diagram. http://www.diagramademarlo.com. Accessed 4 Apr 2021

  25. Marquand, A.: Logical diagrams for n terms. Phil. Mag. 12, 266–270 (1881). https://doi.org/10.1080/14786448108627104

    Article  Google Scholar 

  26. 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: ‘Logic: A History of its Central Concepts, pp. 611–682. North-Holland (2012). https://doi.org/10.1016/B978-0-444-52937-4.50011-3

  27. Pagnan, R.J.: A diagrammatic calculus of syllogisms. J. Log. Lang. Inform. 21(3), 347–364 (2012). https://doi.org/10.1007/s10849-011-9156-7

    Article  MathSciNet  MATH  Google Scholar 

  28. Parsons, T.: The traditional square of opposition. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Summer Edition. Stanford University (2017). https://plato.stanford.edu/archives/sum2017/entries/square/

  29. Peirce, C.S.: Prolegomena to an apology for pragmaticism. Monist 16(4), 492–546 (1906). https://doi.org/10.5840/monist190616436

    Article  Google Scholar 

  30. Peirce, C.S., Hartshorne, C., Weiss, P.: Collected Papers of Charles Sanders Peirce. Harvard University Press, Cambridge (1933)

    Google Scholar 

  31. Riche, N.H., Dwyer, T.: Untangling euler diagrams. IEEE Trans. Vis. Comput. Graph. 16(6), 1090–1099 (2010). https://doi.org/10.1109/TVCG.2010.210

    Article  Google Scholar 

  32. Roberts, D.: The existential graphs of Charles S. Peirce.: Mouton, The Hague (1973)

    Google Scholar 

  33. Shin, S.-J.: Logical Status of Diagrams. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  34. Shin, S.-J.: Heterogeneous reasoning and its logic. Bull. Symb. Log. 10(1), 86 (2004). https://doi.org/10.2178/bsl/1080330275

    Article  MathSciNet  MATH  Google Scholar 

  35. Shin, S.-J., Lemon, O., Mumma, J.: Diagrams. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Summer Edition. Stanford University (2018). https://plato.stanford.edu/archives/sum2018/entries/diagrams/

  36. Strawson, P.F.: Introduction to Logical Theory. Methuen, London (1952)

    MATH  Google Scholar 

  37. Venn, J.: On the diagrammatic and mechanical representation of propositions and reasonings. Lond. Edinb. Dublin Philos. Mag. J. Sci. 10(59), 1–18 (1880). https://doi.org/10.1080/14786448008626877

    Article  Google Scholar 

  38. Venn, J.: Symbolic Logic. MacMillan, London (1881). https://doi.org/10.1037/14127-000

Download references

Author information

Authors and Affiliations

  1. University of Huelva, Huelva, Spain

    Marcos Bautista López Aznar & Walter Federico Gadea

  2. University of Seville, Seville, Spain

    Guillermo Címbora Acosta

Authors
  1. Marcos Bautista López Aznar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guillermo Címbora Acosta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Walter Federico Gadea
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcos Bautista López Aznar .

Editor information

Editors and Affiliations

  1. Saga University, Saga, Japan

    Kohei Arai

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Aznar, M.B.L., Címbora Acosta, G., Gadea, W.F. (2022). Significance in Marlo Diagrams Versus Thoroughness of Venn Diagrams. In: Arai, K. (eds) Intelligent Computing. SAI 2022. Lecture Notes in Networks and Systems, vol 506. Springer, Cham. https://doi.org/10.1007/978-3-031-10461-9_14

Download citation

Publish with us

Policies and ethics

Search

Navigation