Iterated revision and minimal change of conditional beliefs
type: Item
instance of: scholarly article
title: Iterated revision and minimal change of conditional beliefs
zbMATH Open document ID: 0858.03030
DOI: 10.1007/BF00248151
author: Craig Boutilier
published in: Journal of Philosophical Logic
publication date: 1996-10-15T00:00:00Z
review text: In the now classic AGM model of theory change [\textit{C. E. Alchourrón}, \textit{P. Gärdenfors} and \textit{D. Makinson}, J. Symb. Log. 50, 510-530 (1985; Zbl 0578.03011); \textit{P. Gärdenfors}, Knowledge in flux: modeling the dynamics of epistemic states, MIT Press (1988)], no intuitively reasonable account of repeated change seems to be available. Let \(K\) be a belief set and \(\leq\) a relation of entrenchment for \(K\) (or any equivalent mechanism for changing \(K)\). We can regard the pair \(\langle K,\leq\rangle\) as a representation of the current belief state. When an input sentence \(\alpha\) is received, we can use \(\leq\) to obtain the revised belief set \(K^* \alpha\) that replaces \(K\). However, we are not provided with a new entrenchment relation to go with \(K^* \alpha\). In other words, the belief state \(\langle K,\leq \rangle\) is replaced by only an incomplete representation \(\langle K^* \alpha,? \rangle\) of the new belief state. Since we do not now have an entrenchment relation or other mechanism for change, we do not know how to change the new belief state when revision by yet another sentence \(\beta\) is called for. In this paper, the author summarizes and extends previous work in which he introduced a formally elegant and well worked-out solution to this problem. His minimal conditional revision (in earlier work called ``natural revision'') constructs a new mechanism for change by minimal change of the old one. The mechanisms for belief change used in this model are orderings on possible worlds. Intuitively, each such ordering represents an assignment of a degree of implausibility to each world. A belief state can then be represented by a pair consisting of a belief set and an implausibility ordering in which the minimal elements coincide with the worlds that are compatible with the belief set. (An entrenchment relation can easily be derived from such an implausibility ordering.) Actually, the first element of the pair, the belief set,…
reviewed by: Sven Ove Hansson
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 68T27
zbMATH DE Number: 907934
zbMATH Keywords: conditionals
zbMATH Keywords: minimal conditional revision
zbMATH Keywords: belief change
zbMATH Keywords: orderings on possible worlds
zbMATH Keywords: degree of implausibility
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00248151
OpenAlex ID: W2049486611
description: scientific article; zbMATH DE number 907934