Skip to main content
SpringerLink
Log in

Equivalence Proof for Intuitionistic Existential Alpha Graphs

  • Conference paper
  • First Online:
Diagrammatic Representation and Inference (Diagrams 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12909))

Included in the following conference series:

Abstract

We give a formal proof of the mathematical equivalence between a proposed system of existential graphs and intuitionistic propositional calculus. Along the way, we obtain a new set of algebraic rules axiomatizing intuitionistic propositional 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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Chagrov, A., Zakharyaschev, M.: Modal Logic. No. 35 in Oxford Logic Guides. Clarendon Press, Oxford (1997)

    Google Scholar 

  2. Fuentes, C.: Cálculo de secuentes y gráficos existenciales Alfa: Dos estructuras equivalentes para la lógica proposicional. Undergraduate thesis, Universidad del Tolima, Ibagué (Colombia) (2014)

    Google Scholar 

  3. Goldblatt, R.: Topoi. The Categorial Analysis of Logic. Elsevier, Amsterdam (1984)

    MATH  Google Scholar 

  4. Heyting, A.: Intuitionism. An Introduction. North-Holland, Amsterdam (1971)

    MATH  Google Scholar 

  5. Oostra, A.: Los gráficos Alfa de Peirce aplicados a la lógica intuicionista. Cuadernos de Sistemática Peirceana 2, 25–60 (2010)

    Google Scholar 

  6. Oostra, A.: Gráficos existenciales Beta intuicionistas. Cuadernos de Sistemática Peirceana 3, 53–78 (2011)

    Google Scholar 

  7. Oostra, A.: Los gráficos existenciales Gama aplicados a algunas lógicas modales intuicionistas. Cuadernos de Sistemática Peirceana 4, 27–50 (2012)

    Google Scholar 

  8. Oostra, A.: Representación compleja de los gráficos Alfa para la lógica implicativa con conjunción. Boletín de Matemáticas 26(1), 31–50 (2019)

    MathSciNet  Google Scholar 

  9. Ortiz, J., Segura, J.: Gráficos Alfa intuicionistas. Undergraduate thesis, Universidad del Tolima, Ibagué (Colombia) (2018)

    Google Scholar 

  10. Peirce, C.S.: Collected Papers of Charles Sanders Peirce. Harvard University Press, Cambridge (1931–1958). 8 volumes

    Google Scholar 

  11. Peirce, C.S.: Logic of the Future. De Gruyter, Berlin (2019–2021). 3 volumes

    Google Scholar 

  12. Roberts, D.D.: The Existential Graphs of Charles S. Peirce. Mouton, The Hague (1973)

    Book  Google Scholar 

  13. Tarski, A.: Der Aussagenkalkül und die Topologie. Fundamenta Mathematicae 31, 103–134 (1938)

    Article  Google Scholar 

  14. Zalamea, F.: Pragmaticismo, gráficos y continuidad: hacia el lugar de C. S. Peirce en la historia de la lógica. Mathesis 13, 147–156 (1997)

    Google Scholar 

  15. Zalamea, F.: Peirce’s Logic of Continuity. A Conceptual and Mathematical Approach. Docent Press, Boston (2012)

    MATH  Google Scholar 

  16. Zeman, J.J.: The Graphical Logic of C. S. Peirce. Ph.D. dissertation, University of Chicago, Chicago (1964)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidad del Tolima, Ibagué, Colombia

    Arnold Oostra

Authors
  1. Arnold Oostra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arnold Oostra .

Editor information

Editors and Affiliations

  1. Jadavpur University, Kolkata, India

    Amrita Basu

  2. University of Cambridge, Cambridge, UK

    Gem Stapleton

  3. Lancaster University in Leipzig, Leipzig, Germany

    Sven Linker

  4. Deakin University, Burwood, VIC, Australia

    Catherine Legg

  5. Kyoto University, Kyoto, Japan

    Emmanuel Manalo

  6. Universidade Federal Fluminense, NiterĂłi, Brazil

    Petrucio Viana

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Oostra, A. (2021). Equivalence Proof for Intuitionistic Existential Alpha Graphs. In: Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E., Viana, P. (eds) Diagrammatic Representation and Inference. Diagrams 2021. Lecture Notes in Computer Science(), vol 12909. Springer, Cham. https://doi.org/10.1007/978-3-030-86062-2_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-86062-2_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86061-5

  • Online ISBN: 978-3-030-86062-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation