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DOI: 10.4230/LIPIcs.CSL.2025.43

Linear Realisability over Nets: Multiplicatives

Authors: Adrien Ragot, Thomas Seiller, and Lorenzo Tortora de Falco

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract

We provide a new realisability model based on orthogonality for the multiplicative fragment of linear logic, both in presence of generalised axioms (MLL^✠) and in the standard case (MLL). The novelty is the definition of cut elimination for generalised axioms. We prove that our model is adequate and complete both for MLL^✠ and MLL.

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Adrien Ragot, Thomas Seiller, and Lorenzo Tortora de Falco. Linear Realisability over Nets: Multiplicatives. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 43:1-43:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ragot_et_al:LIPIcs.CSL.2025.43,
  author =	{Ragot, Adrien and Seiller, Thomas and Tortora de Falco, Lorenzo},
  title =	{{Linear Realisability over Nets: Multiplicatives}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{43:1--43:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.43},
  URN =		{urn:nbn:de:0030-drops-228002},
  doi =		{10.4230/LIPIcs.CSL.2025.43},
  annote =	{Keywords: Linear Logic, Proof Nets, Realisability, Orthogonality, Hypergraphs, Rewriting, Correctness}
}

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Linear Realisability over Nets: Multiplicatives

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