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DOI: 10.4230/LIPIcs.CSL.2022.35

Planar Realizability via Left and Right Applications

Authors: Haruka Tomita

Published in: LIPIcs, Volume 216, 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)

Abstract

We introduce a class of applicative structures called bi-BDI-algebras. Bi-BDI-algebras are generalizations of partial combinatory algebras and BCI-algebras, and feature two sorts of applications (left and right applications). Applying the categorical realizability construction to bi-BDI-algebras, we obtain monoidal bi-closed categories of assemblies (as well as of modest sets). We further investigate two kinds of comonadic applicative morphisms on bi-BDI-algebras as non-symmetric analogues of linear combinatory algebras, which induce models of exponential and exchange modalities on non-symmetric linear logics.

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Haruka Tomita. Planar Realizability via Left and Right Applications. In 30th EACSL Annual Conference on Computer Science Logic (CSL 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 216, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{tomita:LIPIcs.CSL.2022.35,
  author =	{Tomita, Haruka},
  title =	{{Planar Realizability via Left and Right Applications}},
  booktitle =	{30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-218-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{216},
  editor =	{Manea, Florin and Simpson, Alex},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2022.35},
  URN =		{urn:nbn:de:0030-drops-157558},
  doi =		{10.4230/LIPIcs.CSL.2022.35},
  annote =	{Keywords: Realizability, combinatory algebra, monoidal bi-closed category, exponential modality, exchange modality}
}

Document

DOI: 10.4230/LIPIcs.CSL.2021.38

Realizability Without Symmetry

Authors: Haruka Tomita

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Abstract

In categorical realizability, it is common to construct categories of assemblies and modest sets from applicative structures. In this paper, we introduce several classes of applicative structures and apply the categorical realizability construction to them. Then we obtain closed multicategories, closed categories and skew closed categories, which are more general categorical structures than Cartesian closed categories and symmetric monoidal closed categories. Moreover, we give the necessary and sufficient conditions for obtaining closed multicategories and closed categories of assemblies.

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Haruka Tomita. Realizability Without Symmetry. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{tomita:LIPIcs.CSL.2021.38,
  author =	{Tomita, Haruka},
  title =	{{Realizability Without Symmetry}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.38},
  URN =		{urn:nbn:de:0030-drops-134729},
  doi =		{10.4230/LIPIcs.CSL.2021.38},
  annote =	{Keywords: Realizability, combinatory algebra, closed multicategory, closed category, skew closed category}
}

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Documents authored by Tomita, Haruka

Planar Realizability via Left and Right Applications

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Realizability Without Symmetry

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