A New Syntax for Diagrammatic Logic: A Generic Figures Approach

  • Gianluca CaterinaEmail author
  • Rocco Gangle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11974)


In this paper we propose a new syntactical representation of C.S. Peirce’s diagrammatic systems for propositional and predicate logic. In particular, we use the categorical notion of generic figures to represent the syntax of the diagrammatic language as a category of functors from a suitable, simple category into the category of sets, highlighting the relational nature of Peirce’s diagrammatic logic.


  1. 1.
    Brady, G., Trimble, T.H.: A categorical interpretation of C.S Peirce’s propositional logic alpha. J. Pure Appl. Algebra 149, 213–239 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Caterina, G., Gangle, R.: Iconicity and Abduction. SAPERE, vol. 29. Springer, Cham (2016). Scholar
  3. 3.
    Caterina, G., Gangle, R.: The sheet of indication: a diagrammatic semantics for Peirce’s EG-alpha. Synthese 192(4), 923–940 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Caterina, G., Tohmè, F., Gangle, R.: Abduction: a categorical characterization. J. Appl. Logic 13(1), 78–90 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Coecke, B., Kissinger, A.: Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, Cambridge (2017)CrossRefGoogle Scholar
  6. 6.
    Dau, F.: The Logic System of Concept Graphs with Negation. LNCS (LNAI), vol. 2892. Springer, Heidelberg (2003). Scholar
  7. 7.
    Kauffman, L.: Peirce’s existential graphs. Cybern. Hum. Knowing 18, 49–81 (2001)Google Scholar
  8. 8.
    Ma, M., Pietarinen, A.: Proof analysis of Peirce’s alpha system of graphs. Stud. Logica 105(3), 625–647 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mac Lane, S.: Categories for the Working Mathematician. Springer, New York (1998)zbMATHGoogle Scholar
  10. 10.
    Reyes, M., Reyes, G., Zolfaghari, H.: Generic Figures and their Glueings. Polimetrica, Milan (2004)zbMATHGoogle Scholar
  11. 11.
    Spivak, D.: Category Theory for the Sciences. MIT Press, Cambridge (2014)zbMATHGoogle Scholar
  12. 12.
    Roberts, D.D.: The Existential Graphs of C.S. Peirce. Mouton, The Hague (1973)Google Scholar
  13. 13.
    Sergeyev, Y.D.: Arithmetic of Infinity. Edizioni Orizzonti Meridionali, Cosenza (2003)zbMATHGoogle Scholar
  14. 14.
    Sergeyev, Y.D.: New applied approach for executing computations with infinite and infinitesimal quantities. Informatica 19(4), 567–596 (2008)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Sergeyev, Y.D.: Numerical infinities and infinitesimals: methodology, applications, and repercussions on two Hilbert problems. EMS Surv. Math. Sci. 4, 219–320 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Zeman, J.: Peirce’s logical graphs. Semiotica 12, 239–256 (1974)Google Scholar

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Authors and Affiliations

  1. 1.Endicott CollegeBeverlyUSA

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