Skip to main content
Springer Nature Link
Log in

Constants and Functions in Peirce’s Existential Graphs

  • Conference paper
Conceptual Structures: Knowledge Architectures for Smart Applications (ICCS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4604))

Included in the following conference series:

  • 764 Accesses

Abstract

The system of Peirce’s existential graphs is a diagrammatic version of first order logic. To be more precise: As Peirce wanted to develop a logic of relatives (i.e., relations), existential graphs correspond to first order logic with relations and identity, but without constants or functions. In contemporary elaborations of first order logic, constants and functions are usually employed. In this paper, it is described how the syntax, semantics and calculus for Peirce’s existential graphs has to be extended in order to encompass constants and functions as well.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Burch, R.W.: A Peircean Reduction Thesis: The Foundation of Topological Logic. Texas Tech. University Press, Texas, Lubbock (1991)

    Google Scholar 

  • Chein, M., Mugnier, M.-L.: Conceptual graphs: Fundamental notions. Revue d’Intelligence Artificiell 6, 365–406 (1992)

    Google Scholar 

  • Chein, M., Mugnier, M.-L.: Conceptual graphs are also graphs. Technical report, LIRMM, Université Montpellier II, Rapport de Recherche 95003 (1995)

    Google Scholar 

  • Dau, F.: An embedding of existential graphs into concept graphs with negations. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, pp. 15–19. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  • Dau, F.: The Logic System of Concept Graphs with Negations and its Relationship to Predicate Logic. In: Dau, F. (ed.) The Logic System of Concept Graphs with Negation. LNCS (LNAI), vol. 2892, Springer, Heidelberg (2003)

    Google Scholar 

  • Dau, F.: Fixing shin’s reading algorithm for peirce’s existential graphs. In: Barker-Plummer, D., Cox, R., Swoboda, N. (eds.) Diagrams 2006. LNCS (LNAI), vol. 4045, pp. 88–92. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  • Dau, F.: Mathematical logic with diagrams, based on the existential graphs of peirce. Habilitation thesis (to be published), Available at: http://www.dr-dau.net

  • Dau, F.: The role of existential graphs in peirce’s philosophy. In: Schärfe, H., Hitzler, P., Øhrstrøm, P. (eds.) ICCS 2006. LNCS (LNAI), vol. 4068, pp. 28–41. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  • Dau, F.: Some notes on proofs with alpha graphs. In: Schärfe, H., Hitzler, P., Øhrstrøm, P. (eds.) ICCS 2006. LNCS (LNAI), vol. 4068, pp. 172–188. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  • Dau, F., Eklund, P.: Towards a diagrammatic reasoning system for description logics. Submitted to the Journal of Visual Languages and Computing, Elsevier (2006), Available at http://www.kvocentral.org

  • Hartshorne, W., Burks (eds.): Collected Papers of Charles Sanders Peirce, Harvard University Press, Cambridge, Massachusetts (1931-1935)

    Google Scholar 

  • Peirce, C.S., Sowa, J.F.: Existential Graphs: MS 514 by Charles Sanders Peirce with commentary by John Sowa, 1908 (2000), Available at: http://www.jfsowa.com/peirce/ms514.htm

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

    Google Scholar 

  • Shin, S.-J.: The Iconic Logic of Peirce’s Graphs. Bradford Book, Massachusetts (2002)

    MATH  Google Scholar 

  • Sowa, J.F.: Conceptual structures: information processing in mind and machine. Addison-Wesley, Reading, Mass (1984)

    MATH  Google Scholar 

  • Sowa, J.F.: Conceptual graphs summary. In: Nagle, T.E., Nagle, J.A., Gerholz, L.L., Eklund, P.W. (eds.) Conceptual Structures: current research and practice, pp. 3–51. Ellis Horwood (1992)

    Google Scholar 

  • Sowa, J.F.: Knowledge Representation: Logical, Philosophical, and Computational Foundations, Brooks Cole, Pacific Grove, CA (2000)

    Google Scholar 

  • Zeman, J.J.: The Graphical Logic of C. S. Peirce. PhD thesis, University of Chicago (1964), Available at: http://www.clas.ufl.edu/users/jzeman/

Download references

Author information

Authors and Affiliations

  1. University of Wollongong, Australia

    Frithjof Dau

Authors
  1. Frithjof Dau
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Uta Priss Simon Polovina Richard Hill

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dau, F. (2007). Constants and Functions in Peirce’s Existential Graphs. In: Priss, U., Polovina, S., Hill, R. (eds) Conceptual Structures: Knowledge Architectures for Smart Applications. ICCS 2007. Lecture Notes in Computer Science(), vol 4604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73681-3_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73681-3_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73680-6

  • Online ISBN: 978-3-540-73681-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics