Belief revision, conditional logic and nonmonotonic reasoning
type: Item
instance of: scholarly article
title: Belief revision, conditional logic and nonmonotonic reasoning
zbMATH Open document ID: 0834.03008
author: Wayne Wobcke
published in: Notre Dame Journal of Formal Logic
publication date: 1996-03-31T00:00:00Z
review text: The central concern of this wide-ranging paper is to develop an account of belief revision that follows the general idea of the AGM paradigm, but which also gives us information about iterated revision. The strategy is to take one of the presentations of the well-known AGM approach, namely that in terms of epistemic entrenchment relations, and refine it to ensure that the output of a revision is of the same kind as the input, viz. a belief set with associated entrenchment relation. Specifically, the author proposes a rule for taking any entrenchment relation representable as a ranking into the positive integers, to a new such relation that reassigns the rank of a given formula whilst making ``as little change as possible'' to the ranks of other formulae. Postulates are given for the generated revision operations. The author also discusses questions of computability, and the translation of his rule into the languages of nonmonotonic inference and of conditionals. Reviewer's comments: Readers should take care with the following technical points. (1) Whilst every revision operation on a fixed belief set \(K\) satisfying the AGM postulates \(K^*1\) to \(K^*8\) can be characterized by an epistemic entrenchment relation, not quite all of them can be characterized by the author's ranked epistemic entrenchment relations -- indeed, presumably not all of them can be characterized by well-ordered entrenchment relations. In other words, even in the non- iterative context, the author's construction concerns a slightly proper subset of the AGM functions. (2) On page 66 the author claims that there are no infinite descending chains of ranked epistemic entrenchments under his relation \(\leq\). However, all that is guaranteed by the definition is that any infinite descending chain will have a greatest lower bound -- which need not be an element of the chain unless we assume, for example, that the language admits only finitely many non-equivalent formulae. The author has stated to t…
reviewed by: David Makinson
Mathematics Subject Classification ID: 03B60
zbMATH DE Number: 824593
zbMATH Keywords: belief change
zbMATH Keywords: nonmonotonic reasoning
zbMATH Keywords: belief revision
zbMATH Keywords: AGM
zbMATH Keywords: iterated revision
zbMATH Keywords: epistemic entrenchment relations
zbMATH Keywords: computability
zbMATH Keywords: conditionals
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1040308829
OpenAlex ID: W2092435617
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DOI: 10.1305/NDJFL/1040308829
description: scientific article; zbMATH DE number 824593