Foundational belief change
type: Item
instance of: scholarly article
title: Foundational belief change
zbMATH Open document ID: 0810.03018
DOI: 10.1007/BF01049408
author: Abhaya C. Nayak
published in: Journal of Philosophical Logic
publication date: 1994-11-09T00:00:00Z
review text: An operation of contraction for a set \(A\) of sentences is an operation such that for any sentence \(\alpha\), \(A - \alpha\), the outcome of contracting \(A\) by \(\alpha\), is a subset of \(A\) that does not imply \(\alpha\) (unless \(\alpha\) is logically true). This paper is concerned with the operation \(-\) of contraction on a theory \(K\) that can be derived from an operation \(\div\) of contraction on a base \(B\) for \(K\) (i.e., a set \(B\) such that \(\text{Cn}(B) = K\)) according to the principle \(K - a = \text{Cn} (B \div a)\). The paper starts from previous work by \textit{A. Fuhrmann} [J. Philos. Logic 20, No. 2, 175-203 (1991; Zbl 0723.03010)] in which the operation \(\div\) on the base is essentially a variant of save contraction, as defined by \textit{C. Alchourrón} and \textit{D. Makinson} [Stud. Logica 44, 405-422 (1985; Zbl 0605.03002)]. The author attempts to find conditions on \(\div\) that are sufficient for -- to satisfy the so-called supplementary postulates for rational belief contraction that have been introduced by Peter Gärdenfors. After showing that even quite strong restrictions on Fuhrmann's construction are insufficient to yield these properties, the author introduces a modified construction with the desired properties. This construction involves a modification of safe contraction to make it maxichoice, i.e., to ensure that \(B \div \alpha\) is a maximal subset of \(B\) that does not imply \(\alpha\).
reviewed by: Sven Ove Hansson
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 68T27
zbMATH DE Number: 683098
zbMATH Keywords: belief revision
zbMATH Keywords: theory change
zbMATH Keywords: rational belief contraction
zbMATH Keywords: safe contraction
MaRDI profile type: Publication
cites work: On the logic of theory change: Partial meet contraction and revision functions
cites work: Q3039305
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full work available at URL: https://doi.org/10.1007/bf01049408
OpenAlex ID: W1982886824
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description: scientific article; zbMATH DE number 683098