Finite contractions on infinite belief sets
type: Item
instance of: scholarly article
title: Finite contractions on infinite belief sets
zbMATH Open document ID: 1317.03022
author: Sven Ove Hansson
published in: Studia Logica
publication date: 2013-01-03T00:00:00Z
review text: In classical studies of belief change, a belief set is a set of sentences closed under logical consequence. Thus, a belief set is an infinite entity. However, it is possible to define a special class where the belief set can be represented by a finite set of formulae. A belief set \(K\) is finite-based if and only if it has a finite representation, i.e. if and only if there is a finite set \(A\) of sentences such that \(K = \mathrm{Cn}(A)\). A partial meet contraction is a function that selects the ``best'' elements of the set \(K \bot p\) (maximal subsets of \(K\) that do not imply the sentence \(p\)). These subsets, if the language is not finite, are not finite-based, from which it follows that partial meet contraction does not in general preserving this property. Even if \(K\) is finite-based, the contraction outcome \(K \sim \gamma\;p\) may nevertheless lack a finite representation. The desired property is: \[ \text{If } K \text{ is finite-based, then so is } K \div p \text{ (finite-based outcome).} \] In previous works, the author proved that the AGM contractions that satisfy finite-based outcome exactly coincide with those AGM contractions that can alternatively be constructed as instances of specified meet contraction (contraction based on sentential selection [J. Log. Comput. 17, No. 3, 479--498 (2007; Zbl 1135.03008)] and specified meet contraction [Erkenntnis 69, No. 1, 31--54 (2008; Zbl 1155.03010)]). In this paper, Hansson extends these results to belief sets that are not finite-based.
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 6121542
zbMATH Keywords: specified meet contraction
zbMATH Keywords: finitely contextual contraction
zbMATH Keywords: belief change
zbMATH Keywords: contraction
zbMATH Keywords: finite contraction
reviewed by: Eduardo Fermé
MaRDI profile type: Publication
full work available at URL: s11225-012-9440-9
OpenAlex ID: W2060036376
cites work: On the logic of theory change: Partial meet contraction and revision functions
cites work: Q3039305
cites work: Relevance sensitive belief structures
cites work: A textbook of belief dynamics. Theory change and database updating
cites work: Contraction Based on Sentential Selection
cites work: Specified meet contraction
cites work: Global and iterated contraction and revision: an exploration of uniform and semi-uniform approaches
cites work: Local change
cites work: Parallel interpolation, splitting, and relevance in belief change
cites work: Q4518818
DOI: 10.1007/S11225-012-9440-9
Recommended article: Theory contraction and base contraction unified
Recommended article: Q4225112
Recommended article: A model for structural changes of belief
Recommended article: Maximal and perimaximal contraction
Recommended article: Blockage contraction
Recommended article: An Axiomatic Characterization of Ensconcement-Based Contraction
Recommended article: Contraction Based on Sentential Selection
Recommended article: Specified meet contraction
Recommended article: On a logico-algebraic approach to AGM belief contraction theory
Recommended article: Q4546703
description: scientific article; zbMATH DE number 6121542