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Documents authored by Tortora de Falco, Lorenzo

Document
DOI: 10.4230/LIPIcs.FSCD.2025.16
Yeo’s Theorem for Locally Colored Graphs: the Path to Sequentialization in Linear Logic

Authors: Rémi Di Guardia, Olivier Laurent, Lorenzo Tortora de Falco, and Lionel Vaux Auclair

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
We revisit sequentialization proofs associated with the Danos-Regnier correctness criterion in the theory of proof nets of linear logic. Our approach relies on a generalization of Yeo’s theorem for graphs, based on colorings of half-edges. This happens to be the appropriate level of abstraction to extract sequentiality information from a proof net without modifying its graph structure. We thus obtain different ways of recovering a sequent calculus derivation from a proof net inductively, by relying on a splitting ⅋-vertex, on a splitting ⊗-vertex, on a splitting terminal vertex, etc. The proof of our Yeo-style theorem relies on a key lemma that we call cusp minimization. Given a coloring of half-edges, a cusp in a path is a vertex whose adjacent half-edges in the path have the same color. And, given a cycle with at least one cusp and subject to suitable hypotheses, cusp minimization constructs a cycle with strictly less cusps. In the absence of cusp-free cycles, cusp minimization is then enough to ensure the existence of a splitting vertex, i.e. a vertex that is a cusp of any cycle it belongs to. Our theorem subsumes several graph-theoretical results, including some known to be equivalent to Yeo’s theorem. The novelty is that they can be derived in a straightforward way, just by defining a dedicated coloring, again without any modification of the underlying graph structure (vertices and edges) - similar results from the literature required more involved encodings.
Cite as

Rémi Di Guardia, Olivier Laurent, Lorenzo Tortora de Falco, and Lionel Vaux Auclair. Yeo’s Theorem for Locally Colored Graphs: the Path to Sequentialization in Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{diguardia_et_al:LIPIcs.FSCD.2025.16,
  author =	{Di Guardia, R\'{e}mi and Laurent, Olivier and Tortora de Falco, Lorenzo and Vaux Auclair, Lionel},
  title =	{{Yeo’s Theorem for Locally Colored Graphs: the Path to Sequentialization in Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.16},
  URN =		{urn:nbn:de:0030-drops-236317},
  doi =		{10.4230/LIPIcs.FSCD.2025.16},
  annote =	{Keywords: Linear Logic, Proof Net, Sequentialization, Graph Theory, Yeo’s Theorem}
}
Document
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.
Cite as

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}
}
Document
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.
Cite as

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}
}
Document
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.
Cite as

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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