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.MFCS.2018.9
URN: urn:nbn:de:0030-drops-95917
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9591/
Go to the corresponding LIPIcs Volume Portal

Burel, Guillaume

Linking Focusing and Resolution with Selection

pdf-format:
LIPIcs-MFCS-2018-9.pdf (0.4 MB)

Abstract

Focusing and selection are techniques that shrink the proof search space for respectively sequent calculi and resolution. To bring out a link between them, we generalize them both: we introduce a sequent calculus where each occurrence of an atom can have a positive or a negative polarity; and a resolution method where each literal, whatever its sign, can be selected in input clauses. We prove the equivalence between cut-free proofs in this sequent calculus and derivations of the empty clause in that resolution method. Such a generalization is not semi-complete in general, which allows us to consider complete instances that correspond to theories of any logical strength. We present three complete instances: first, our framework allows us to show that ordinary focusing corresponds to hyperresolution and semantic resolution; the second instance is deduction modulo theory; and a new setting, not captured by any existing framework, extends deduction modulo theory with rewriting rules having several left-hand sides, which restricts even more the proof search space.

BibTeX - Entry

@InProceedings{burel:LIPIcs:2018:9591,
  author =	{Guillaume Burel},
  title =	{{Linking Focusing and Resolution with Selection}},
  booktitle =	{43rd International Symposium on Mathematical Foundations  of Computer Science (MFCS 2018)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Igor Potapov and Paul Spirakis and James Worrell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9591},
  URN =		{urn:nbn:de:0030-drops-95917},
  doi =		{10.4230/LIPIcs.MFCS.2018.9},
  annote =	{Keywords: logic in computer science, automated deduction, proof theory, sequent calculus, refinements of resolution, deduction modulo theory, polarization}
}

Keywords: logic in computer science, automated deduction, proof theory, sequent calculus, refinements of resolution, deduction modulo theory, polarization
Collection: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)
Issue Date: 2018
Date of publication: 27.08.2018

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI