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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.


  Abstract

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


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