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DOI: 10.4230/LIPIcs.CSL.2020.24

Glueability of Resource Proof-Structures: Inverting the Taylor Expansion

Authors: Giulio Guerrieri, Luc Pellissier, and Lorenzo Tortora de Falco

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract

A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof-structure, through a rewriting system acting both on resource and MELL proof-structures.

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Giulio Guerrieri, Luc Pellissier, and Lorenzo Tortora de Falco. Glueability of Resource Proof-Structures: Inverting the Taylor Expansion. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{guerrieri_et_al:LIPIcs.CSL.2020.24,
  author =	{Guerrieri, Giulio and Pellissier, Luc and Tortora de Falco, Lorenzo},
  title =	{{Glueability of Resource Proof-Structures: Inverting the Taylor Expansion}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.24},
  URN =		{urn:nbn:de:0030-drops-116674},
  doi =		{10.4230/LIPIcs.CSL.2020.24},
  annote =	{Keywords: linear logic, Taylor expansion, proof-net, natural transformation}
}

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DOI: 10.4230/LIPIcs.FSCD.2016.20

Computing Connected Proof(-Structure)s From Their Taylor Expansion

Authors: Giulio Guerrieri, Luc Pellissier, and Lorenzo Tortora de Falco

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

Abstract

We show that every connected Multiplicative Exponential Linear Logic (MELL) proof-structure (with or without cuts) is uniquely determined by a well-chosen element of its Taylor expansion: the one obtained by taking two copies of the content of each box. As a consequence, the relational model is injective with respect to connected MELL proof-structures.

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Giulio Guerrieri, Luc Pellissier, and Lorenzo Tortora de Falco. Computing Connected Proof(-Structure)s From Their Taylor Expansion. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{guerrieri_et_al:LIPIcs.FSCD.2016.20,
  author =	{Guerrieri, Giulio and Pellissier, Luc and Tortora de Falco, Lorenzo},
  title =	{{Computing Connected Proof(-Structure)s From Their Taylor Expansion}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{20:1--20:18},
  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.2016.20},
  URN =		{urn:nbn:de:0030-drops-60031},
  doi =		{10.4230/LIPIcs.FSCD.2016.20},
  annote =	{Keywords: proof-nets, (differential) linear logic, relational model, Taylor expansion}
}

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Documents authored by Tortora de Falco, Lorenzo

Glueability of Resource Proof-Structures: Inverting the Taylor Expansion

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Computing Connected Proof(-Structure)s From Their Taylor Expansion

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