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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2012.320
URN: urn:nbn:de:0030-drops-36815
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3681/
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Hetzl, Stefan ; Straßburger, Lutz

Herbrand-Confluence for Cut Elimination in Classical First Order Logic

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Abstract

We consider cut-elimination in the sequent calculus for classical first-order logic. It is well known that this system, in its most general form, is neither confluent nor strongly normalizing. In this work we take a coarser (and mathematically more realistic) look at cut-free proofs. We analyze which witnesses they choose for which quantifiers, or in other words: we only consider the Herbrand-disjunction of a cut-free proof. Our main theorem is a confluence result for a natural class of proofs: all (possibly infinitely many) normal forms of the non-erasing reduction lead to the same Herbrand-disjunction.

BibTeX - Entry

@InProceedings{hetzl_et_al:LIPIcs:2012:3681,
  author =	{Stefan Hetzl and Lutz Stra{\ss}burger},
  title =	{{Herbrand-Confluence for Cut Elimination in Classical First Order Logic}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{320--334},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{Patrick C{\'e}gielski and Arnaud Durand},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3681},
  URN =		{urn:nbn:de:0030-drops-36815},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.CSL.2012.320},
  annote =	{Keywords: proof theory, first-order logic, tree languages, term rewriting, semantics of proofs}
}

Keywords: proof theory, first-order logic, tree languages, term rewriting, semantics of proofs
Seminar: Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL
Issue Date: 2012
Date of publication: 27.08.2012


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