On Translations of Epsilon Proofs to LK

Matthias Baaz; Anela Lolic

doi:10.29007/9pts

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On Translations of Epsilon Proofs to LK

14 pages•Published: May 26, 2024

Matthias Baaz and Anela Lolic

Abstract

In this paper we present the proof that there is no elementary translation from cut- free derivations in the sequent calculus variant of the epsilon calculus to LK-proofs with bounded cut-complexity. This is a partial answer to a question by Toshiyasu Arai. Fur- thermore, we show that the intuitionistic format of the sequent calculus variant of the epsilon calculus is not sound for intuitionistic logic, due to the presence of all classical quantifier-shift rules.

Keyphrases: epsilon calculus, Hilbert's epsilon formalism, sequent calculus

In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 232--245

Links:	https://easychair.org/publications/paper/qhXDJ
	https://doi.org/10.29007/9pts

BibTeX entry

@inproceedings{LPAR2024:On_Translations_of_Epsilon,
  author    = {Matthias Baaz and Anela Lolic},
  title     = {On Translations of Epsilon Proofs to LK},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bj\{\textbackslash{}o\}rner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  pages     = {232--245},
  year      = {2024},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/qhXDJ},
  doi       = {10.29007/9pts}}

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