Counterfactuals in Nelson Logic

  • Andreas Kapsner
  • Hitoshi Omori
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10455)


We motivate and develop an extension of Nelson’s constructive logic N3 that adds a counterfactual conditional to the existing setup. After developing the semantics, we will outline how our account will be able to give a nice analysis of natural language counterfactuals. In particular, the account does justice to the intuitions and arguments that have lead Alan Hájek to claim that most conditionals are false, but assertable, without actually forcing us to endorse that rather uncomfortable claim.



Hitoshi Omori is a Postdoctoral Research Fellow of Japan Society for the Promotion of Science (JSPS). We would like to thank the anonymous referees for their helpful comments that improved our paper. We would also like to thank Massimiliano Carrara, Roberto Ciuni, and the participants of Kyoto Philosophical Logic Workshop I for useful comments and discussions.


  1. 1.
    Dunn, M.: Intuitive semantics for first-degree entailments and ‘coupled trees’. Philos. Stud. 29(3), 149–168 (1976)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gabbay, D., Kurucz, A., Wolter, F., Zakharyaschev, M.: Many-Dimensional Modal Logics: Theory and Applications (2003)Google Scholar
  3. 3.
    Hájek, A.: Most counterfactuals are false. Unpublished draft
  4. 4.
    Kamide, N., Wansing, H.: Proof Theory of N4-Related Paraconsistent Logics. Studies in Logic, vol. 54. College Publications, London (2015)zbMATHGoogle Scholar
  5. 5.
    Kapsner, A.: Logics and Falsifications. Trends in Logic, vol. 40. Springer, Heidelberg (2014)zbMATHGoogle Scholar
  6. 6.
    Lewis, D.K.: Counterfactuals. Blackwell, Boston (1973)zbMATHGoogle Scholar
  7. 7.
    Odintsov, S.P.: Constructive Negations and Paraconsistency. Trends in Logic, vol. 26. Springer, Heidelberg (2008)CrossRefzbMATHGoogle Scholar
  8. 8.
    Omori, H.: A simple connexive extension of the basic relevant logic BD. IfCoLog J. Logics Appl. 3(3), 467–478 (2016)Google Scholar
  9. 9.
    Omori, H.: From paraconsistent logic to dialetheic logic. In: Andreas, H., Verdée, P. (eds.) Logical Studies of Paraconsistent Reasoning in Science and Mathematics. TL, vol. 45, pp. 111–134. Springer, Cham (2016). doi: 10.1007/978-3-319-40220-8_8 CrossRefGoogle Scholar
  10. 10.
    Pizzi, C.: Boethius’ thesis and conditional logic. J. Philos. Logic 6, 283–302 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Priest, G.: Negation as cancellation and connexive logic. Topoi 18(2), 141–148 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Priest, G.: An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge University Press, Cambridge (2008)CrossRefzbMATHGoogle Scholar
  13. 13.
    Segerberg, K.: Notes on conditional logic. Stud. Logica 48(2), 157–168 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Sider, T.: Logic for Philosophy. Oxford University Press, Oxford (2010)Google Scholar
  15. 15.
    Unterhuber, M.: Beyond system P - Hilbert-style convergence results for conditional logics with a connexive twist. IfCoLog J. Logics Appl. 3(3), 377–412 (2016)Google Scholar
  16. 16.
    Wansing, H.: Semantics-based nonmonotonic inference. Notre Dame J. Formal Logic 36(1), 44–54 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Wansing, H.: Connexive modal logic. In: Schmidt, R., Pratt-Hartmann, I., Reynolds, M., Wansing, H. (eds.) Advances in Modal Logic, vol. 5, pp. 367–383. King’s College Publications, London (2005)Google Scholar
  18. 18.
    Wansing, H.: A note on negation in categorial grammar. Logic J. IGPL 15, 271–286 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Wansing, H.: Connexive logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2014). Fall 2014 edition

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of PhilosophyLMU MunichMunichGermany
  2. 2.Department of PhilosophyKyoto UniversityKyotoJapan

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