Skip to main content

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

  • Chapter
  • First Online:
  • 641 Accesses

Part of the book series: Studies in Universal Logic ((SUL))

Abstract

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.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   89.99
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

Learn about institutional subscriptions

References

  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. A.R. Anderson, N.D. Belnap, Entailment: The Logic of Relevance and Necessity, vol. 1 (Princeton University Press, Princeton, 1975)

    Google Scholar 

  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. Apuleius, Peri Hermeneias, Opera Quae Supersunt, Vol. III: De Philosophia Libri, ed. by C. Moreschini (Teubner, Stuttgart/Leipzig, 1991)

    Google Scholar 

  5. St.T. Aquinas, Summa Theologica, Second part of the second part (Benziger Brothers, New York, 1947); Translated by Fathers of the English Dominican Province

    Google Scholar 

  6. Boethius, Commentaries on, On Interpretation, ed. by C. Meiser (Teubner, Leipzig, 1880/1887)

    Google Scholar 

  7. P. Cintula, Weakly implicative (fuzzy) logics I: basic properties. Arch. Math. Log. 45, 673–704 (2006)

    Google Scholar 

  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)

    Article  Google Scholar 

  9. G. Lakoff, Hedges: a study in meaning criteria and the logic of fuzzy concepts. J. Philos. Log. 2, 458–508 (1973)

    Article  Google Scholar 

  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.341–362

    Google Scholar 

  11. G.J.C. Lokhorst, Anderson’s relevant deontic and eubouliatic systems. Notre Dame J. Formal Log. 49, 65–7 (2008)

    Google Scholar 

  12. G. Metcalfe, F.Montagna, Substructural fuzzy logics. J. Symb. Log. 72, 834–864 (2007)

    Article  Google Scholar 

  13. J. Slaney, MaGIC: matrix generator for implication connectives, version 2.2.1. http://users.cecs.anu.edu.au/jks/magic.html (2008)

  14. V. Vychodil, Truth-depressing hedges and BL-logic. Fuzzy Sets Syst. 157, 2074–2090 (2006)

    Article  Google Scholar 

  15. N. Webster, An American Dictionary of the English Language, vol. 2 (S. Converse, New York, 1828)

    Google Scholar 

  16. E. Yang, R, fuzzy R, and algebraic Kripke-style semantics. Korean J. Log. 15, 207–221 (2012)

    Google Scholar 

  17. E. Yang, R and relevance principle revisited. J. Philos. Log. 42, 767–782 (2013)

    Google Scholar 

  18. E. Yang, Algebraic Kripke-style semantics for relevance logics. J. Philos. Log. 43, 803–826 (2014)

    Article  Google Scholar 

  19. E. Yang, Substructural fuzzy-relevance logic. Notre Dame J. Formal Log. 56, 471–491 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gert-Jan C. Lokhorst .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Lokhorst, GJ.C. (2017). Fuzzy Eubouliatic Logic: A Fuzzy Version of Anderson’s Logic of Prudence. In: Béziau, JY., Basti, G. (eds) The Square of Opposition: A Cornerstone of Thought. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-45062-9_19

Download citation

Publish with us

Policies and ethics