Fuzzy Eubouliatic Logic: A Fuzzy Version of Anderson’s Logic of Prudence

  • Gert-Jan C. LokhorstEmail author
Part of the Studies in Universal Logic book series (SUL)


Alan Ross Anderson was one of the first logicians who were interested in the logic of prudence and related concepts, such as caution. He called this area “eubouliatic logic,” a term which has not become popular. Anderson made a distinction between four prudence-related concepts which can be placed in a square of opposition. Prudence and related concepts are nowadays often seen as fuzzy concepts. We investigate which consequences this has for the logic of these concepts.


Eubouliatic logic Fuzzy logic Modal logic Prudence Relevance logic Square of opposition 

Mathematics Subject Classification (2000)

Primary 03B47; Secondary 03B52 


  1. 1.
    A.R. Anderson, A new square of opposition: eubouliatic logic, in Akten des XIV. Internationalen Kongresses für Philosophie, vol. 2 (Herder, Vienna, 1968)Google Scholar
  2. 2.
    A.R. Anderson, N.D. Belnap, Entailment: The Logic of Relevance and Necessity, vol. 1 (Princeton University Press, Princeton, 1975)Google Scholar
  3. 3.
    A.R. Anderson, N.D. Belnap, J.M. Dunn, Entailment: The Logic of Relevance and Necessity, vol. 2 (Princeton University Press, Princeton, 1992)Google Scholar
  4. 4.
    Apuleius, Peri Hermeneias, Opera Quae Supersunt, Vol. III: De Philosophia Libri, ed. by C. Moreschini (Teubner, Stuttgart/Leipzig, 1991)Google Scholar
  5. 5.
    St.T. Aquinas, Summa Theologica, Second part of the second part (Benziger Brothers, New York, 1947); Translated by Fathers of the English Dominican ProvinceGoogle Scholar
  6. 6.
    Boethius, Commentaries on, On Interpretation, ed. by C. Meiser (Teubner, Leipzig, 1880/1887)Google Scholar
  7. 7.
    P. Cintula, Weakly implicative (fuzzy) logics I: basic properties. Arch. Math. Log. 45, 673–704 (2006)Google Scholar
  8. 8.
    W.L. Gombocz, Apuleius is better still: a correction to the square of opposition [De Interpretatione 180, 19–181, 7 Thomas]. Mnemosyne 43, 124–131 (1990)CrossRefGoogle Scholar
  9. 9.
    G. Lakoff, Hedges: a study in meaning criteria and the logic of fuzzy concepts. J. Philos. Log. 2, 458–508 (1973)CrossRefGoogle Scholar
  10. 10.
    W. Lenzen, Leibniz on alethic and deontic modal logic, in Leibniz et les puissances du langage, ed. by D.Berlioz, F.Nez (Vrin, Paris, 2005), pp.341–362Google Scholar
  11. 11.
    G.J.C. Lokhorst, Anderson’s relevant deontic and eubouliatic systems. Notre Dame J. Formal Log. 49, 65–7 (2008)Google Scholar
  12. 12.
    G. Metcalfe, F.Montagna, Substructural fuzzy logics. J. Symb. Log. 72, 834–864 (2007)CrossRefGoogle Scholar
  13. 13.
    J. Slaney, MaGIC: matrix generator for implication connectives, version 2.2.1. (2008)
  14. 14.
    V. Vychodil, Truth-depressing hedges and BL-logic. Fuzzy Sets Syst. 157, 2074–2090 (2006)CrossRefGoogle Scholar
  15. 15.
    N. Webster, An American Dictionary of the English Language, vol. 2 (S. Converse, New York, 1828)Google Scholar
  16. 16.
    E. Yang, R, fuzzy R, and algebraic Kripke-style semantics. Korean J. Log. 15, 207–221 (2012)Google Scholar
  17. 17.
    E. Yang, R and relevance principle revisited. J. Philos. Log. 42, 767–782 (2013)Google Scholar
  18. 18.
    E. Yang, Algebraic Kripke-style semantics for relevance logics. J. Philos. Log. 43, 803–826 (2014)CrossRefGoogle Scholar
  19. 19.
    E. Yang, Substructural fuzzy-relevance logic. Notre Dame J. Formal Log. 56, 471–491 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Faculty of Technology, Policy and ManagementDelft University of TechnologyDelftThe Netherlands

Personalised recommendations