Skip to main content
SpringerLink
Log in

Rasiowa–Harrop Disjunction Property

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

We show that there is a purely proof-theoretic proof of the Rasiowa–Harrop disjunction property for the full intuitionistic propositional calculus (\(\mathbf {IPC}\)), via natural deduction, in which commuting conversions are not needed. Such proof is based on a sound and faithful embedding of \(\mathbf {IPC}\) into an atomic polymorphic system. This result strengthens a homologous result for the disjunction property of \(\mathbf {IPC}\) (presented in a recent paper co-authored with Fernando Ferreira) and answers a question then posed by Pierluigi Minari.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dinis, B., and G. Ferreira, Instantiation overflow, Reports on Mathematical Logic 51:15–33, 2016.

    Google Scholar 

  2. Ferreira, F., Comments on predicative logic, Journal of Philosophical Logic 35:1–8, 2006.

    Article  Google Scholar 

  3. Ferreira, F., and G. Ferreira, Commuting conversions vs. the standard conversions of the “good” connectives, Studia Logica 92:63–84, 2009.

    Article  Google Scholar 

  4. Ferreira, F., and G. Ferreira, Atomic polymorphism, The Journal of Symbolic Logic 78:260–274, 2013.

    Article  Google Scholar 

  5. Ferreira, F., and G. Ferreira, The faithfulness of \({{\bf F}}_{{\bf at}}\): a proof-theoretic proof, Studia Logica 103(6):1303–1311, 2015.

    Article  Google Scholar 

  6. Ferreira, G., Eta-conversions of \({\bf IPC} \) implemented in atomic \({\bf F}\), To appear in Logic Jnl IGPL, published online July 1, 2016. doi:10.1093/jigpal/jzw035.

  7. Girard, J.-Y., Y. Lafont, and P. Taylor, Proofs and Types, Cambridge University Press, 1989.

    Google Scholar 

  8. Minari, P., and A. Wronski, The property (HD) in intermediate logics. A partial solution of a problem of H. Ono, Reports on Mathematical Logic 22:21–25, 1988.

    Google Scholar 

  9. Prawitz, D., Natural Deduction, Almkvist & Wiksell, Stockholm, 1965. Reprinted, with a new preface, in Dover Publications, 2006.

  10. Reynolds, J. C., Towards a theory of type structure, in B. Robinet (ed.), Lecture Notes in Computer Science, vol. 19, Colloque sur la programmation, Springer, 1974, pp. 408–425.

  11. Russell, B., Principles of Mathematics, 2nd edn., George Allen and Unwin, London, 1903 (1937).

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, Ed. C6, 1749-016, Lisbon, Portugal

    Gilda Ferreira

Authors
  1. Gilda Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gilda Ferreira.

Additional information

Presented by Jacek Malinowski

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ferreira, G. Rasiowa–Harrop Disjunction Property. Stud Logica 105, 649–664 (2017). https://doi.org/10.1007/s11225-016-9704-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-016-9704-x

Keywords

Search

Navigation