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DOI: 10.4230/LIPIcs.FSCD.2026.29

Absolute Convergence and Taylor Expansion in Web Based Models of Linear Logic

Authors: Christine Tasson and Aymeric Walch

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract

We provide in this paper a generic construction of web models of linear logic with partial sums. Our construction captures a wide class of orthogonality models, ranging from coherence spaces to probabilistic coherence spaces, finiteness spaces and Köthe spaces. All these models are built on the same principles, but were very heterogeneous in the specificities of their technical development. Our construction factorizes these specificities, allowing a unified treatment of further developments, such as differentiation and Taylor expansion. The differential λ-calculus relates quantitative aspects of programs to differentiation and to Taylor expansion in models of linear logic. Recent work has generalized the axioms of Taylor expansion, so that they apply to many models that only feature partial sums. However, that work did not cover Köthe spaces and finiteness spaces. We generalize the theory of Taylor expansion to models in which coefficients can be negative, and we prove that our generic web models always satisfy this new axiomatization. Therefore, all the aforementioned models feature a Taylor expansion.

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Christine Tasson and Aymeric Walch. Absolute Convergence and Taylor Expansion in Web Based Models of Linear Logic. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 29:1-29:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{tasson_et_al:LIPIcs.FSCD.2026.29,
  author =	{Tasson, Christine and Walch, Aymeric},
  title =	{{Absolute Convergence and Taylor Expansion in Web Based Models of Linear Logic}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{29:1--29:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.29},
  URN =		{urn:nbn:de:0030-drops-263794},
  doi =		{10.4230/LIPIcs.FSCD.2026.29},
  annote =	{Keywords: Categorical semantics, Linear Logic, Quantitative semantics, Taylor expansion}
}

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Absolute Convergence and Taylor Expansion in Web Based Models of Linear Logic

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