License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2015.110
URN: urn:nbn:de:0030-drops-54103
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5410/
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Hetzl, Stefan ; Zivota, Sebastian

Tree Grammars for the Elimination of Non-prenex Cuts

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Abstract

Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs with prenex Pi_1-cuts in classical first-order logic corresponds to computing the language of a particular type of tree grammars. The present paper extends this connection to arbitrary (i.e. non-prenex) cuts without quantifier alternations. The key to treating non-prenex cuts lies in using a new class of tree grammars, constraint grammars, which describe the relationship of the applicability of its productions by a propositional formula.

BibTeX - Entry

@InProceedings{hetzl_et_al:LIPIcs:2015:5410,
  author =	{Stefan Hetzl and Sebastian Zivota},
  title =	{{Tree Grammars for the Elimination of Non-prenex Cuts}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{110--127},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Stephan Kreutzer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5410},
  URN =		{urn:nbn:de:0030-drops-54103},
  doi =		{10.4230/LIPIcs.CSL.2015.110},
  annote =	{Keywords: proof theory, cut-elimination, Herbrand's theorem, tree grammars}
}

Keywords: proof theory, cut-elimination, Herbrand's theorem, tree grammars
Collection: 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)
Issue Date: 2015
Date of publication: 07.09.2015

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