A Galois connection approach to superposition and inaccessibility
type: Item
instance of: scholarly article
title: A Galois connection approach to superposition and inaccessibility
zbMATH Open document ID: 0810.03049
DOI: 10.1007/BF00673001
author: Jeremy Butterfield
author: Joseph Melia
published in: International Journal of Theoretical Physics
publication date: 1995-04-20T00:00:00Z
review text: The authors consider ``superposition'' and ``accessibility'' in terms of the lattices generated by these relations over the power set of states. Thus superposition is the relation between states of finding wffs certain in that state, and this relation induces a Galois connection which in turn induces a closure map on the power set of states. Similarly inaccessibility is understood as the relation between states of making opposite predictions about a wff, and this too induces a Galois connection and hence induces a closure map on the power set of states. The purpose of this paper is to use the theory of Galois connections to provide a sufficient condition for the complete lattices induced by these two closure maps to coincide. A short introduction to Galois connections is included in the paper, proofs are indicated, though not detailed, and there is a useful section relating this work to that of others. According to the authors, this paper is in the tradition of Varadarajan, among others, but is novel in that it uses Galois connections to establish this result. Perhaps more importantly, the authors do not assume that the lattice \(L\) of ``events'' (the ``yes-no'' propositions) is orthomodular, nor that states are probability-measures on \(L\), or that the set of states be \(\sigma\)- convex.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06A15
zbMATH DE Number: 575501
zbMATH Keywords: accessibility
zbMATH Keywords: power set of states
zbMATH Keywords: superposition
zbMATH Keywords: Galois connection
zbMATH Keywords: closure map
zbMATH Keywords: inaccessibility
zbMATH Keywords: complete lattices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 575501