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DOI: 10.4230/LIPIcs.CSL.2025.44

Classical Linear Logic in Perfect Banach Lattices

Authors: Pedro H. Azevedo de Amorim, Leon Witzman, and Dexter Kozen

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

Abstract

In recent years, researchers have proposed various models of linear logic with strong connections to measure theory, with probabilistic coherence spaces (PCoh) being one of the most prominent. One of the main limitations of the PCoh model is that it cannot interpret continuous measures. To overcome this obstacle, Ehrhard has extended PCoh to a category of positive cones and linear Scott-continuous functions and shown that it is a model of intuitionistic linear logic. In this work we show that the category PBanLat₁ of perfect Banach lattices and positive linear functions of norm at most 1 can serve the same purpose, with some added benefits. We show that PBanLat₁ is a model of classical linear logic (without exponential) and that PCoh embeds fully and faithfully in PBanLat₁ while preserving the monoidal and *-autonomous structures. Finally, we show how PBanLat₁ can be used to give semantics to a higher-order probabilistic programming language.

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Pedro H. Azevedo de Amorim, Leon Witzman, and Dexter Kozen. Classical Linear Logic in Perfect Banach Lattices. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 44:1-44:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{azevedodeamorim_et_al:LIPIcs.CSL.2025.44,
  author =	{Azevedo de Amorim, Pedro H. and Witzman, Leon and Kozen, Dexter},
  title =	{{Classical Linear Logic in Perfect Banach Lattices}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{44:1--44:21},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-228013},
  doi =		{10.4230/LIPIcs.CSL.2025.44},
  annote =	{Keywords: Probabilistic Semantics, Linear Logic, Categorical Semantics}
}

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Documents authored by Azevedo de Amorim, Pedro H.

Classical Linear Logic in Perfect Banach Lattices

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