Severe withdrawal (and recovery)
type: Item
instance of: scholarly article
title: Severe withdrawal (and recovery)
zbMATH Open document ID: 0934.03024
DOI: 10.1023/A:1004344003217
author: Hans Rott
author: Maurice Pagnucco
published in: Journal of Philosophical Logic
publication date: 2000-04-25T00:00:00Z
review text: The authors undertake a comprehensive study of a motivated variant of AGM contraction. The motivation is that if we reduce a belief set \(K\) by eliminating one of its elements \(x\), then we should not retain any elements \(y\) of \(K\) whose credibility, from the point of view of \(K\), is less than or equal to that of \(x\). With this motivation for the concept of `severe withdrawal', the most direct definition is in terms of the Gärdenfors-Makinson apparatus of `epistemic entrenchment', as was already suggested by the first of the authors under review in his paper ``Two methods of constructing contractions and revisions of knowledge systems'' [J. Philos. Log. 20, No. 2, 149-173 (1991; Zbl 0723.03009)]. Indeed, such a definition of severe withdrawal \(K-x\) as \(\{y\in K:x<y\}\) where \(<\) is an epistemic entrenchment relation (in the principal case that \(x\in K\) and \(x\notin Cn(\emptyset))\) is formally simpler and also easier to motivate than the corresponding definition of AGM contraction as \(\{y\in K:x<x\vee y\}\). In the paper under review, the authors examine the operation of severe withdrawal from several angles familiar from the literature on AGM belief revision operations. As well as the definition in terms of epistemic entrenchment, they consider that of nested spheres of possible worlds (following a 1991 suggestion of S. Lindström and W. Rabinowicz), and also that of the syntactic principles or `postulates' satisfied by the operation (on which some work had already been carried out by \textit{E. L. Fermé} and \textit{R. O. Rodriguez} [``A brief note about Rott contraction'', Log. J. IGPL 6, No. 6, 835-842 (1998; Zbl 0923.03041)]). In the context of nested spheres, \(K-x\) is determined by adding to the \(K\)-worlds not only the closest \(\neg x\)-worlds (as for AGM contraction) but also all those \(x\)-worlds that are at least as close to \(K\) as are the closest \(\neg x\)-worlds. On the level of syntactic properties satisfied, the controversial …
reviewed by: David Makinson
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 1383887
zbMATH Keywords: variant of AGM contraction
zbMATH Keywords: severe withdrawal
zbMATH Keywords: epistemic entrenchment
zbMATH Keywords: belief revision
zbMATH Keywords: nested spheres of possible worlds
zbMATH Keywords: syntactic principles
zbMATH Keywords: AGM principle of recovery
zbMATH Keywords: antitony principle
Wikidata QID: Q29026579
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1383887