Truth-tracking by belief revision
type: Item
instance of: scholarly article
title: Truth-tracking by belief revision
zbMATH Open document ID: 1439.03039
author: Alexandru Baltag
author: Nina Gierasimczuk
author: Sonja Smets
published in: Studia Logica
publication date: 2019-11-29T00:00:00Z
review text: Call plausibility space a triple of the form \((S,\mathcal{O},\preceq)\) where \(\mathcal{O}\), the set of observables, is a set of subsets of \(S\), the set of possible worlds, with both \(S\) and \(\mathcal{O}\) being countable and \(\bigcap\{o\in\mathcal{O}\mid s\in o\}=\{s\}\) for all \(s\in S\), and where \(\preceq\) is a total pre-order over \(S\), with \(s\preceq t\) meant to express that \(s\) is at least as plausible as \(t\). An iterative revision method \(R\) maps a pair consisting of a plausibility space and an observable to a plausibility space; given a plausibility space \(\mathbb S\) and a sequence \(\sigma=(o_1,\dots,o_k)\) of members of \(\mathcal{O}\), \(R(\mathbb S,\sigma)\) is then inductively defined as \(\mathbb S\) if \(k=0\), and as \(R\Bigl(R\bigl(\mathbb S,(o_1,\dots,o_{k-1})\bigr),o_k\Bigr)\) otherwise; any set of possible worlds that are all minimal in \(R(\mathbb S,\sigma)\) is then identified as a proposition that is believed after observing \(o_1\), \dots, \(o_k\). A number of properties of \(R\) are considered, that have to hold for any \(\mathbb S\), \(k\geq 1\) and \(o_1\), \dots, \(o_k\), in particular: \begin{itemize} \item conservative if \(o_k\) is believed in case it is believed after seeing \(o_1\), \dots, \(o_{k-1}\); \item strongly conservative if the plausibility spaces after seeing \(o_1\), \dots, \(o_{k-1}\) and after seeing \(o_1\), \dots, \(o_k\) are the same in case \(o_k\) is believed after seeing \(o_1\), \dots, \(o_{k-1}\). \end{itemize} Also, 3 specific one-step revision methods are defined (the conditions bring no change to the set of observations): \begin{itemize} \item [COND] (for conditioning): the total preorder of \(R(\mathbb S,o)\) is the restriction of the total preorder of \(\mathbb S\) to the set of possible worlds of \(R(\mathbb S,o)\), which are the possible worlds of \(\mathbb S\) that belong to \(o\). \item [LEX] (for lexicographic revision): the possible worlds of \(R(\mathbb S,o)\) are those of \(\m…
reviewed by: Éric Martin
Mathematics Subject Classification ID: 03B42
zbMATH DE Number: 7138883
zbMATH Keywords: belief revision
zbMATH Keywords: dynamic epistemic logic
zbMATH Keywords: formal learning theory
zbMATH Keywords: truth-tracking
MaRDI profile type: Publication
full work available at URL: s11225-018-9812-x
OpenAlex ID: W2189130216
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DOI: 10.1007/S11225-018-9812-X
description: scientific article; zbMATH DE number 7138883