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DOI: 10.4230/LIPIcs.FSCD.2023.26

Type Isomorphisms for Multiplicative-Additive Linear Logic

Authors: Rémi Di Guardia and Olivier Laurent

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract

We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus for ⋆-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo [Vincent Balat and Roberto Di Cosmo, 1999]. This yields a much richer equational theory involving distributivity and annihilation laws. The unit-free case is obtained by relying on the proof-net syntax introduced by Hughes and Van Glabbeek [Dominic Hughes and Rob van Glabbeek, 2005]. We then use the sequent calculus to extend our results to full MALL (including all units).

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Rémi Di Guardia and Olivier Laurent. Type Isomorphisms for Multiplicative-Additive Linear Logic. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 26:1-26:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{diguardia_et_al:LIPIcs.FSCD.2023.26,
  author =	{Di Guardia, R\'{e}mi and Laurent, Olivier},
  title =	{{Type Isomorphisms for Multiplicative-Additive Linear Logic}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{26:1--26:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.26},
  URN =		{urn:nbn:de:0030-drops-180103},
  doi =		{10.4230/LIPIcs.FSCD.2023.26},
  annote =	{Keywords: Linear Logic, Type Isomorphisms, Multiplicative-Additive fragment, Proof nets, Sequent calculus, Star-autonomous categories with finite products}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2016.25

Focusing in Orthologic

Authors: Olivier Laurent

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)

Abstract

We propose new sequent calculus systems for orthologic (also known as minimal quantum logic) which satisfy the cut elimination property. The first one is a very simple system relying on the involutive status of negation. The second one incorporates the notion of focusing (coming from linear logic) to add constraints on proofs and thus to facilitate proof search. We demonstrate how to take benefits from the new systems in automatic proof search for orthologic.

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Olivier Laurent. Focusing in Orthologic. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{laurent:LIPIcs.FSCD.2016.25,
  author =	{Laurent, Olivier},
  title =	{{Focusing in Orthologic}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.25},
  URN =		{urn:nbn:de:0030-drops-59805},
  doi =		{10.4230/LIPIcs.FSCD.2016.25},
  annote =	{Keywords: orthologic, focusing, minimal quantum logic, linear logic, automatic proof search, cut elimination}
}

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Type Isomorphisms for Multiplicative-Additive Linear Logic

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Focusing in Orthologic

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