License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2022.35
URN: urn:nbn:de:0030-drops-157558
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15755/
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Tomita, Haruka

Planar Realizability via Left and Right Applications

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LIPIcs-CSL-2022-35.pdf (0.7 MB)

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.

BibTeX - Entry

@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/opus/volltexte/2022/15755},
  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}
}

Keywords: Realizability, combinatory algebra, monoidal bi-closed category, exponential modality, exchange modality
Collection: 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)
Issue Date: 2022
Date of publication: 27.01.2022

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