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Journal of Logic and Computation Advance Access published online on August 25, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp040
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Eskolemization in Intuitionistic Logic

Matthias Baaz

Institute for Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, 1040 Vienna, Austria. E-mail:baaz{at}logic.at

Rosalie Iemhoff

Department of Philosophy, University Utrecht, Heidelberglaan 8,3584 CS Utrecht, The Netherlands. E-mail:rosalie.iemhoff{at}phil.uu.nl

Received 29 January 2009.

In Baaz and Iemhoff (2006, Annals of Pure and Applied Logic, 142, 269–295), an alternative skolemization method called eskolemization was introduced that is sound and complete for existence logic with respect to existential quantifiers. Existence logic is a conservative extension of intuitionistic logic by an existence predicate. Therefore, eskolemization provides a skolemization method for intuitionistic logic as well. All proofs in Baaz and Iemhoff (2006, Annals of Pure and Applied Logic, 142, 269–295) were semantical. In this article, a proof-theoretic proof of the completeness of eskolemization with respect to existential quantifiers is presented.

Keywords: Skolemization; eskolemization; orderization; Herbrand's theorem; intuitionistic logic; existence logic; Gentzen calculi



References

  1. Baaz M, Iemhoff. R. Gentzen calculi for the existence predicate. StudiaLogica (2006) 82:7–23.
  2. Baaz M, Iemhoff. R. On the Skolemization of existential quantifiers in intuitionistic logic. Annals of Pure and Applied Logic (2006) 142:269–295.
  3. Baaz M, Iemhoff. R. On Skolemization in constructive theories. Journal of SymbolicLogic (2008) 73:969–998.
  4. Scott. DS. Identity and existence in intuitionistic logic. In: Applications of Sheaves, Proc. Res. Symp. Durham 1977—Fourman MP, et al, eds. (1979) Heidelberg. 660–696. Vol. 753 of Lecture Notes in Mathematics.
  5. Troelstra AS, Schwichtenberg. H. Basic Proof Theory. Cambridge Tracts in Theoretical Computer Science 43 (1996) Cambridge University Press.

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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
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Right arrow Email this article to a friend
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Right arrow Add to My Personal Archive
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Google Scholar
Right arrow Articles by Baaz, M.
Right arrow Articles by Iemhoff, R.
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What's this?