Relations of epistemic proximity for belief change
type: Item
instance of: scholarly article
title: Relations of epistemic proximity for belief change
zbMATH Open document ID: 1319.03037
author: Sven Ove Hansson
published in: Artificial Intelligence
publication date: 2014-10-27T00:00:00Z
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 6362036
zbMATH Keywords: belief change
zbMATH Keywords: descriptor revision
zbMATH Keywords: epistemic proximity
zbMATH Keywords: believability relation
zbMATH Keywords: entrenchment relation
zbMATH Keywords: epistemic entrenchment
reviewed by: Mauricio Reis
MaRDI profile type: Publication
full work available at URL: j.artint.2014.08.001
OpenAlex ID: W2074689653
cites work: On the logic of theory change: Partial meet contraction and revision functions
cites work: On the logic of theory change: safe contraction
cites work: Q3107917
cites work: Q3495345
cites work: Contraction, Revision, Expansion: Representing Belief Change Operations
cites work: Descriptor revision
cites work: Change, choice and inference. A study of belief revision and nonmonotonic reasoning
cites work: Safe Contraction Revisited
DOI: 10.1016/J.ARTINT.2014.08.001
review text: The author proposed in [Stud. Log. 102, No. 5, 955--980 (2014; Zbl 1339.03017)] a new belief change operation known as descriptor revision which has the most well-known change operations (namely, revision, contraction, multiple contraction, etc.) as special cases. This approach relies on a metalinguistic operator \(\mathfrak{B}\) which is interpreted as the belief predicate in the sense that, for any sentence \(p\) in the object language, \(\mathfrak{B} p\) means that \(p\) is believed. A descriptor is then defined as a set of truth-functional combinations of expressions of the form \(\mathfrak{B} p\) and the descriptor revision is presented as an operation which is such that the result of the descriptor revision of a belief set \(K\) by a descriptor \(\Psi\), denoted \(K \circ \Psi\), is a belief set that satisfies the (success) condition expressed by the descriptor \(\Psi\). In the mentioned paper, a class of descriptor revision operations -- namely the relational descriptor revisions -- was introduced. The definition of these functions makes use of a total ordering on the set composed by the belief sets which are outcomes of revision by some descriptor.NEWLINENEWLINEIn the paper under review, a certain class of binary relations on descriptors, called relations of epistemic proximity is formally introduced and a way of defining descriptor revisions by means of these relations is provided. One of the main results of the paper is the equivalence between the descriptor revisions based on relations of epistemic proximity introduced in this paper and the relational descriptor revisions mentioned above. Moreover, this fact is proven by presenting explicit constructions of a relation of epistemic proximity \(\succeq\) from a total ordering \(\leqq\) on the set of descriptor revision outcomes and vice versa, which are such that the descriptor revisions based on \(\succeq\) coincides with the relational descriptor revisions defined by means of \(\leqq\).NEWLINENEWLINEThe a…
description: scientific article; zbMATH DE number 6362036