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.2017.9
URN: urn:nbn:de:0030-drops-77008
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7700/
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Aler Tubella, Andrea ; Guglielmi, Alessio ; Ralph, Benjamin

Removing Cycles from Proofs

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LIPIcs-CSL-2017-9.pdf (0.5 MB)

Abstract

If we track atom occurrences in classical propositional proofs in deep inference, we see that they can form cyclic structures between cuts and identity steps. These cycles are an obstacle to a very natural form of normalisation, that simply unfolds all the contractions in a proof. This mechanism, which we call ‘decomposition’, has many points of contact with explicit substitutions in lambda calculi. In the presence of cycles, decomposition does not terminate, and this is an obvious drawback if we want to interpret proofs computationally. One way of eliminating cycles is eliminating cuts. However, we could ask ourselves whether it is possible to eliminate cycles independently of (general) cut elimination. This paper shows an efficient way to do so, therefore establishing the independence of decomposition from cut elimination. In other words, cut elimination in propositional logic can be separated into three separate procedures: 1) cycle elimination, 2) unfolding of contractions, 3) elimination of cuts in the linear fragment.

BibTeX - Entry

@InProceedings{alertubella_et_al:LIPIcs:2017:7700,
  author =	{Andrea Aler Tubella and Alessio Guglielmi and Benjamin Ralph},
  title =	{{Removing Cycles from Proofs}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Valentin Goranko and Mads Dam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7700},
  URN =		{urn:nbn:de:0030-drops-77008},
  doi =		{10.4230/LIPIcs.CSL.2017.9},
  annote =	{Keywords: proof theory, deep inference, proof complexity}
}

Keywords: proof theory, deep inference, proof complexity
Collection: 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)
Issue Date: 2017
Date of publication: 16.08.2017

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