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Planar Realizability via Left and Right Applications

Author Haruka Tomita

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Author Details

Haruka Tomita
  • Research Institute for Mathematical Sciences, Kyoto University, Japan

Funding

  • Tomita, Haruka: This work was supported by JST ERATO Grant Number JPMJER1603, Japan.

Acknowledgements

I would like to thank Masahito Hasegawa for a lot of helpful discussions and comments. I am also grateful to Naohiko Hoshino for useful advice. Thanks also to anonymous reviewers for their helpful feedback.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.CSL.2022.35

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
Keywords
  • Realizability
  • combinatory algebra
  • monoidal bi-closed category
  • exponential modality
  • exchange modality

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