Localic sup-lattices and tropological systems.
type: Item
instance of: scholarly article
title: Localic sup-lattices and tropological systems.
zbMATH Open document ID: 1060.06022
DOI: 10.1016/S0304-3975(02)00702-8
author: Pedro Resende
author: Steven Vickers
published in: Theoretical Computer Science
publication date: 2004-03-14T00:00:00Z
review text: Approaches to process semantics using quantales and modules over them were developed by the second author of this paper and S.~Abramsky, and (in a slightly different way) by the first author. In these approaches, although the `set' of actions is taken to be a quantale, the set of states remains an untopologized set. In order to give a fully constructive account of these structures, it is necessary not merely to topologize the state set but to replace it with a locale (or `pointless space'): this is done in the present paper. The authors begin by recalling how the `classical' duality for sup-lattices may be constructivized by using localic sup-lattices instead of topological ones, and then go on to indicate how the same approach may be applied to the `tropological systems' introduced by the first author as a setting for process semantics. This enables them to rewrite the `third completeness' results of Abramsky and the second author in constructive form.
Mathematics Subject Classification ID: 06F07
Mathematics Subject Classification ID: 68Q85
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 03F65
Mathematics Subject Classification ID: 06D22
zbMATH DE Number: 2055979
zbMATH Keywords: Quantale
zbMATH Keywords: Localic sup-lattice
zbMATH Keywords: Localic quantale module
zbMATH Keywords: Localic tropological
zbMATH Keywords: system
zbMATH Keywords: Process semantics
zbMATH Keywords: Third completeness
reviewed by: Peter Johnstone
MaRDI profile type: Publication
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full work available at URL: s0304-3975(02)00702-8
OpenAlex ID: W2124170184
description: scientific article; zbMATH DE number 2055979