Chu spaces as a semantic bridge between linear logic and mathematics.
type: Item
instance of: scholarly article
title: Chu spaces as a semantic bridge between linear logic and mathematics.
zbMATH Open document ID: 1042.18002
DOI: 10.1016/S0304-3975(01)00169-4
published in: Theoretical Computer Science
publication date: 2003-07-29T00:00:00Z
review text: The author has for some time been a strong advocate of the usefulness of categories of Chu spaces in both pure mathematics and theoretical computer science. In the present paper, he gives a brief but clear overview of the constructions and basic properties of the `big' and `little' Chu categories \(\mathcal{C}hu (\mathcal{S}et,\Sigma)\) and \(chu(\mathcal{S}et,\Sigma)\). He then shows how they may be used for modelling linear logic, and also describes how arbitrary small categories may be concretely embedded in \(\mathcal{C}hu (\mathcal{S}et,\Sigma)\) for suitable \(\Sigma\). His thesis is that linear logic is `the categorical logic of general mathematics', just as intuitionistic categorical logic is `the categorical logic of cartesian closed mathematics', and that just as \(\mathcal{S}et\) is the `exemplar category' of the latter, so \(\mathcal{C}hu (\mathcal {S}et,-)\) is the exemplar category of general mathematics.
Mathematics Subject Classification ID: 18B15
Mathematics Subject Classification ID: 03F52
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 08A02
Mathematics Subject Classification ID: 18D15
zbMATH DE Number: 1956199
zbMATH Keywords: Chu spaces
zbMATH Keywords: linear logic
zbMATH Keywords: universal mathematics
author: Vaughan R. Pratt
reviewed by: Peter Johnstone
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1956199