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.FSCD.2018.10
URN: urn:nbn:de:0030-drops-91800
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9180/
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Bellin, Gianluigi ; Heijltjes, Willem B.

Proof Nets for Bi-Intuitionistic Linear Logic

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LIPIcs-FSCD-2018-10.pdf (0.5 MB)

Abstract

Bi-Intuitionistic Linear Logic (BILL) is an extension of Intuitionistic Linear Logic with a par, dual to the tensor, and subtraction, dual to linear implication. It is the logic of categories with a monoidal closed and a monoidal co-closed structure that are related by linear distributivity, a strength of the tensor over the par. It conservatively extends Full Intuitionistic Linear Logic (FILL), which includes only the par.
We give proof nets for the multiplicative, unit-free fragment MBILL-. Correctness is by local rewriting in the style of Danos contractibility, which yields sequentialization into a relational sequent calculus extending the existing one for FILL. We give a second, geometric correctness condition combining Danos-Regnier switching and Lamarche's Essential Net criterion, and demonstrate composition both inductively and as a one-off global operation.

BibTeX - Entry

@InProceedings{bellin_et_al:LIPIcs:2018:9180,
  author =	{Gianluigi Bellin and Willem B. Heijltjes},
  title =	{{Proof Nets for Bi-Intuitionistic Linear Logic}},
  booktitle =	{3rd International Conference on Formal Structures for  Computation and Deduction (FSCD 2018)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{H{\'e}l{\`e}ne Kirchner},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9180},
  URN =		{urn:nbn:de:0030-drops-91800},
  doi =		{10.4230/LIPIcs.FSCD.2018.10},
  annote =	{Keywords: proof nets, intuitionistic linear logic, contractibility, linear logic}
}

Keywords: proof nets, intuitionistic linear logic, contractibility, linear logic
Collection: 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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