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.2020.6
URN: urn:nbn:de:0030-drops-116490
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11649/
Go to the corresponding LIPIcs Volume Portal

Acclavio, Matteo ; Maieli, Roberto

Generalized Connectives for Multiplicative Linear Logic

pdf-format:
LIPIcs-CSL-2020-6.pdf (0.6 MB)

Abstract

In this paper we investigate the notion of generalized connective for multiplicative linear logic. We introduce a notion of orthogonality for partitions of a finite set and we study the family of connectives which can be described by two orthogonal sets of partitions.
We prove that there is a special class of connectives that can never be decomposed by means of the multiplicative conjunction ⊗ and disjunction ⅋, providing an infinite family of non-decomposable connectives, called Girard connectives. We show that each Girard connective can be naturally described by a type (a set of partitions equal to its double-orthogonal) and its orthogonal type. In addition, one of these two types is the union of the types associated to a family of MLL-formulas in disjunctive normal form, and these formulas only differ for the cyclic permutations of their atoms.

BibTeX - Entry

@InProceedings{acclavio_et_al:LIPIcs:2020:11649,
  author =	{Matteo Acclavio and Roberto Maieli},
  title =	{{Generalized Connectives for Multiplicative Linear Logic}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11649},
  URN =		{urn:nbn:de:0030-drops-116490},
  doi =		{10.4230/LIPIcs.CSL.2020.6},
  annote =	{Keywords: Linear Logic, Partitions Sets, Proof Nets, Sequent Calculus}
}

Keywords: Linear Logic, Partitions Sets, Proof Nets, Sequent Calculus
Collection: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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