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.RTA.2015.127
URN: urn:nbn:de:0030-drops-51935
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5193/
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Das, Anupam ; Straßburger, Lutz

No complete linear term rewriting system for propositional logic

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Abstract

Recently it has been observed that the set of all sound linear inference rules in propositional logic is already coNP-complete, i.e. that every Boolean tautology can be written as a (left- and right-) linear rewrite rule. This raises the question of whether there is a rewriting system on linear terms of propositional logic that is sound and complete for the set of all such rewrite rules. We show in this paper that, as long as reduction steps are polynomial-time decidable, such a rewriting system does not exist unless coNP=NP.
We draw tools and concepts from term rewriting, Boolean function theory and graph theory in order to access the required intermediate results. At the same time we make several connections between these areas that, to our knowledge, have not yet been presented and constitute a rich theoretical framework for reasoning about linear TRSs for propositional logic.

BibTeX - Entry

@InProceedings{das_et_al:LIPIcs:2015:5193,
  author =	{Anupam Das and Lutz Stra{\ss}burger},
  title =	{{No complete linear term rewriting system for propositional logic}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{127--142},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Maribel Fern{\'a}ndez},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5193},
  URN =		{urn:nbn:de:0030-drops-51935},
  doi =		{10.4230/LIPIcs.RTA.2015.127},
  annote =	{Keywords: Linear rules, Term rewriting, Propositional logic, Proof theory, Deep inference}
}

Keywords: Linear rules, Term rewriting, Propositional logic, Proof theory, Deep inference
Collection: 26th International Conference on Rewriting Techniques and Applications (RTA 2015)
Issue Date: 2015
Date of publication: 18.06.2015

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