1 Search Results for "Dawson, Jeremy"

Document
DOI: 10.4230/LIPIcs.CSL.2013.197
Annotation-Free Sequent Calculi for Full Intuitionistic Linear Logic

Authors: Ranald Clouston, Jeremy Dawson, Rajeev Goré, and Alwen Tiu

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

Abstract
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex annotations to guarantee soundness and cut-elimination. We give a simple and annotation-free display calculus for FILL which satisfies Belnap’s generic cut-elimination theorem. To do so, our display calculus actually handles an extension of FILL, called Bi-Intuitionistic Linear Logic (BiILL), with an ‘exclusion’ connective defined via an adjunction with par. We refine our display calculus for BiILL into a cut-free nested sequent calculus with deep inference in which the explicit structural rules of the display calculus become admissible. A separation property guarantees that proofs of FILL formulae in the deep inference calculus contain no trace of exclusion. Each such rule is sound for the semantics of FILL, thus our deep inference calculus and display calculus are conservative over FILL. The deep inference calculus also enjoys the subformula property and terminating backward proof search, which gives the NP-completeness of BiILL and FILL.
Cite as

Ranald Clouston, Jeremy Dawson, Rajeev Goré, and Alwen Tiu. Annotation-Free Sequent Calculi for Full Intuitionistic Linear Logic. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 197-214, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@InProceedings{clouston_et_al:LIPIcs.CSL.2013.197,
  author =	{Clouston, Ranald and Dawson, Jeremy and Gor\'{e}, Rajeev and Tiu, Alwen},
  title =	{{Annotation-Free Sequent Calculi for Full Intuitionistic Linear Logic}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{197--214},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.197},
  URN =		{urn:nbn:de:0030-drops-41981},
  doi =		{10.4230/LIPIcs.CSL.2013.197},
  annote =	{Keywords: Linear logic, display calculus, nested sequent calculus, deep inference}
}
  • Refine by Author
  • 1 Clouston, Ranald
  • 1 Dawson, Jeremy
  • 1 Goré, Rajeev
  • 1 Tiu, Alwen

  • Refine by Classification

  • Refine by Keyword
  • 1 Linear logic
  • 1 deep inference
  • 1 display calculus
  • 1 nested sequent calculus

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2013

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact