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Herbrand Disjunctions, Cut Elimination and Context-Free Tree Grammars

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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 in first-order predicate logic involving Pi_1-cuts corresponds to computing the language of a particular class of regular tree grammars. The present paper expands this connection to the level of Pi_2-cuts. Given a proof pi of a Sigma_1 formula with cuts only on Pi_2 formulŠ, we show there is associated to pi a natural context-free tree grammar whose language is finite and yields a Herbrand disjunction for pi.

BibTeX - Entry

@InProceedings{afshari_et_al:LIPIcs:2015:5151,
  author =	{Bahareh Afshari and Stefan Hetzl and Graham E. Leigh},
  title =	{{Herbrand Disjunctions, Cut Elimination and Context-Free Tree Grammars}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{1--16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Thorsten Altenkirch},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5151},
  URN =		{urn:nbn:de:0030-drops-51516},
  doi =		{10.4230/LIPIcs.TLCA.2015.1},
  annote =	{Keywords: Classical logic, Context-free grammars, Cut elimination, First-order logic, Herbrand's theorem, Proof theory}
}

Keywords: Classical logic, Context-free grammars, Cut elimination, First-order logic, Herbrand's theorem, Proof theory
Seminar: 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)
Issue date: 2015
Date of publication: 2015


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