A survey of multiple contractions
type: Item
instance of: scholarly article
title: A survey of multiple contractions
zbMATH Open document ID: 0791.03014
DOI: 10.1007/BF01066356
author: André Fuhrmann
author: Sven Ove Hansson
published in: Journal of Logic, Language and Information
publication date: 1994-07-07T00:00:00Z
review text: The authors extend the AGM account of belief contraction [as set out by \textit{C. E. Alchourrón}, \textit{P. Gärdenfors} and \textit{D. Makinson} in ``On the logic of theory change: partial meet contraction and revision functions'', J. Symb. Logic 50, 510-530 (1985; Zbl 0578.03011)] to multiple contraction, i.e. contraction by a set \(A\) of sentences rather than by a single sentence. This should not be confused with iterated contraction, which is another possible extension of the AGM theory, where one considers the result of making one contraction after another. Two principal kinds of multiple contraction are distinguished -- package contraction in which all the sentences in \(A\) are removed from the belief set, and choice contraction in which at least one of them is removed. The authors provide semantic definitions of both kinds using natural generalizations of the AGM ``partial meet'' operations, and also give them both syntactic characterizations in terms of natural generalizations of the ``basic postulates'' of AGM. They observe that in general, neither package nor choice contraction can be reduced to contraction by a single sentence. Even when \(A\) is finite, package contraction still resists such reduction, whilst in that case choice contraction reduces trivially to contraction of the conjunction of all the sentences in \(A\). The presentation is extremely clear, with the authors taking the time to discuss adequately the intuitive background to each formal operation. As they remark, their paper is only a beginning of a study of the subject, and they list several respects in which existing theory for the singleton case, as already developed by Alchourrón, Gärdenfors and Makinson, still awaits extension to the multiple case. These include relationally constrained partial meet contraction and its characterization by ``supplementary postulates'', revision and its relation to contraction via the Levi and Harper identities, and the Makinson/Gärdenfors translatio…
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 502990
zbMATH Keywords: theory change
zbMATH Keywords: belief contraction
zbMATH Keywords: multiple contraction
zbMATH Keywords: belief change
Wikidata QID: Q29302557
reviewed by: David Makinson
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01066356
OpenAlex ID: W1972689493
DBLP publication ID: journals/jolli/FuhrmannH94
description: scientific article; zbMATH DE number 502990