Equilibrium graphs

  • Pedro CabalarEmail author
  • Carlos Pérez
  • Gilberto Pérez


In this paper we present an extension of Peirce’s existential graphs to provide a diagrammatic representation of expressions in Quantified Equilibrium Logic (QEL). Using this formalisation, logical connectives are replaced by encircled regions (circles and squares) and quantified variables are represented as “identity” lines. Although the expressive power is equivalent to that of QEL, the new representation can be useful for illustrative or educational purposes.


Logic programming Answer set programming Diagrammatic reasoning Existential graphs Equilibrium logic 

Mathematics Subject Classification (2010)

03B20 03B55 03B70 68N17 68T27 68T30 


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  1. 1.
    Aguado, F., Cabalar, P., Pearce, D., Pérez, G., Vidal, C.: A denotational semantics for equilibrium logic. Theory Pract. Logic Program. 15(4-5), 620–634 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Brewka, G., Eiter, T., Truszczyński, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)CrossRefGoogle Scholar
  3. 3.
    Febbraro, O., Reale, K., Ricca, F.: A visual interface for drawing ASP programs. In: Faber, W., Leone, N. (eds.) Proceedings of the 25th Italian Conference on Computational Logic, Rende, Italy, July 7-9, 2010, CEUR Workshop Proceedings (2010)Google Scholar
  4. 4.
    Ferraris, P., Lee, J., Lifschitz, V.: A new perspective on stable models. In: Veloso, M.M. (ed.) IJCAI 2007, Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, January 6-12, pp. 372–379 (2007)Google Scholar
  5. 5.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Proceedings of the 5th International Conference on Logic Programming (ICLP’88), pp. 1070–1080, Seattle, Washington (1988)Google Scholar
  6. 6.
    Heyting, A.: Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie der Wissenschaften Physikalisch-mathematische Klasse (1930)Google Scholar
  7. 7.
    Marek, V.W., Truszczyński, M.: Stable models and an alternative logic programming paradigm. In: Apt, K.R., Marek, V.W., Truszczynski, M., Warren, D.S. (eds.) The Logic Programming Paradigm. Artificial Intelligence. Springer, Berlin (1999)Google Scholar
  8. 8.
    Niemelä, I.: Logic programs with stable model semantics as a constraint programming paradigm. Ann. Math. Artif. Intell. 25(3-4), 241–273 (1999)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Peano, G.: Aritmetices principia nova methoda exposita, Torino: Bocca (1889)Google Scholar
  10. 10.
    Pearce, D.: A new logical characterisation of stable models and answer sets. In: Proceedings of Non-Monotonic Extensions of Logic Programming (NMELP’96), pp. 57–70, Bad Honnef, Germany (1996)Google Scholar
  11. 11.
    Pearce, D., Valverde, A.: Quantified equilibrium logic and foundations for answer set programs. In: Proceedings of the 24th International Conference on Logic Programming, ICLP 2008, (Udine, Italy, December 9-13), vol. 5366 of Lecture Notes in Computer Science, pp. 546–560. Springer (2008)Google Scholar
  12. 12.
    Peirce, C.S.: Manuscripts on existential graphs. In: Collected Papers of Charles Sanders Peirce, vol. 4, pp. 320–410. Harvard University Press, Cambridge (1906)Google Scholar
  13. 13.
    Shin, S.-J.: The iconic logic of Peirce’s graphs. Bradford Book (2002)Google Scholar
  14. 14.
    Sowa, J.F.: Conceptual graphs for a data base interface. IBM J. Res. Dev. 20(4), 336–357 (1976)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Sowa, J.F.: Conceptual graphs. In: van Harmelen, F., Lifschitz, V., Porter, B.W. (eds.) Handbook of Knowledge Representation, vol. 3 of Foundations of Artificial Intelligence, pp. 213–237. Elsevier (2008)Google Scholar
  16. 16.
    Sowa, J.F.: From existential graphs to conceptual graphs. IJCSSA 1(1), 39–72 (2013)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of A CoruñaCoruñaSpain

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