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A Sequent-Calculus Based Formulation of the Extended First Epsilon Theorem

  • Matthias Baaz
  • Alexander Leitsch
  • Anela LolicEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10703)

Abstract

The optimal calculation of Herbrand disjunctions from unformalized or formalized mathematical proofs is one of the most prominent problems of computational proof theory. The up-to-date most direct approach to calculate Herbrand disjunctions is based on Hilbert’s epsilon formalism (which is in fact also the oldest framework for proof theory). The algorithm to calculate Herbrand disjunctions is an integral part of the proof of the extended first epsilon theorem. This paper connects epsilon proofs and sequent calculus derivations with cuts. This leads to an improved notation for the epsilon formalism and a computationally improved version of the extended first epsilon theorem, which allows a nonelementary speed-up of the computation of Herbrand disjunctions.

Keywords

Extended first epsilon theorem Herbrand disjunctions Epsilon calculus 

Notes

Acknowledgments

Partially supported by FWF grants P-26976-N25, I-2671-N35 and the Czech-Austrian project MOBILITY No. 7AMB17AT054.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of Discrete Mathematics and Geometry 104TU WienViennaAustria
  2. 2.Institute of Computer Languages (E185)TU WienViennaAustria

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