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The Exact Intuitionistic Meaning of the Square of Opposition

  • Joseph Vidal-RossetEmail author
Chapter
Part of the Studies in Universal Logic book series (SUL)

Abstract

This paper aims at providing a complete analysis of the intuitionistic version of the square of opposition and a reply to an article published by Mélès (Around and Beyond the Square of Opposition, ed. by J.-Y. Béziau, D. Jacquette (Studies in Universal Logic, Birkhaüser, 2012), pp. 201–218) on the same topic.

Keywords

Intuitionistic logic Square of opposition Tableau methods 

Mathematics Subject Classification (2000)

Primary 03B20 03F03; Secondary 03B10 

Notes

Acknowledgements

Many thanks to

• Baptiste Mélès both for the discussions we had about the intuitionistic version of the square of opposition and for his very useful remarks on a draft of my paper,

• Jean-Yves Béziau who gave to me the occasion of writing this paper,

• My institution, the Archives Poincaré, which funded my participation to the fourth conference on the square of opposition (Vatican, May 5–9, 2014),

• the referees of the final version of this paper.

References

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    J. Bell, G. Solomon, D. DeVidi, Logical Options: An Introduction to Classical and Alternative Logics (Broadview Press, Peterborough, 2001)Google Scholar
  2. 2.
    J.-Y. Béziau, D. Jacquette (eds.), Around and Beyond the Square of Opposition (Studies in Universal Logic, Birkhaüser, 2012)Google Scholar
  3. 3.
    R. David, K. Nour, C. Raffalli, Introduction à la Logique: Théorie de la Démonstration (Dunod, Paris, 2004)Google Scholar
  4. 4.
    B. Mélès, No group of opposition for constructive logics: the intuitionistic and linear cases, in Around and Beyond the Square of Opposition, ed. by J.-Y. Béziau, D. Jacquette (Studies in Universal Logic, Birkhaüser, 2012), pp. 201–218CrossRefGoogle Scholar
  5. 5.
    J. von Plato, Elements of Logical Reasoning (Cambridge University Press, Cambridge, 2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Philosophy DepartmentLorraine UniversityNancyFrance

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