The logic of justified belief, explicit knowledge, and conclusive evidence
type: Item
instance of: scholarly article
title: The logic of justified belief, explicit knowledge, and conclusive evidence
zbMATH Open document ID: 1300.03015
author: Alexandru Baltag
author: Bryan Renne
author: Sonja Smets
published in: Annals of Pure and Applied Logic
publication date: 2014-01-13T00:00:00Z
reviewed by: Éric Martin
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 6244764
zbMATH Keywords: dynamic epistemic logic
zbMATH Keywords: justification logic
zbMATH Keywords: belief revision
zbMATH Keywords: logical omniscience
zbMATH Keywords: Gettier
zbMATH Keywords: evidence
MaRDI profile type: Publication
full work available at URL: j.apal.2013.07.005
OpenAlex ID: W2048792847
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DOI: 10.1016/J.APAL.2013.07.005
review text: The aim of the paper is to develop a \textit{theory of explicitly justified knowledge based on the actual availability of conclusive evidence}. It consists of a logical propositional framework built over [\textit{A. Baltag} et al., Lect. Notes Comput. Sci. 7456, 168--190 (2012; Zbl 1362.03012)], with two modal operators \(K\) and \(\square\), with \(K\varphi\) meant to capture that \(\varphi\) follows from the ``hard'' information received by an underlying agent, and \(\square\varphi\) meant to capture that the agent defeasibly knows \(\varphi\).NEWLINENEWLINESemantically, given a set of possible worlds \(W\) and \(w\in W\), \(K\varphi\) is true at \(w\) if \(\varphi\) is true at \(v\) for all \(v\in W\) with \(v\sim w\) where \(\sim\) is an equivalence relation over \(W\) (\(v\sim w\) indicates that \(v\) and \(w\) cannot be distinguished under the currently available information), and \(\square\varphi\) is true at \(w\) if \(\varphi\) is true at \(v\) for all \(v\in W\) with \(w\geq v\), where \(\geq\) is a preorder relation over \(W\) (\(w\geq v\) indicates that \(v\) is at least as plausible as \(w\)); worlds \(\sim\)-equivalent are supposed to be \(\geq\)-comparable, and conversely. The language also contains terms built over the set of terms of the form \(c_\varphi\), where \(\varphi\) is a propositional formula, and closed under two operators, \(\cdot\) and \(+\). Such a term \(t\) is supposed to represent a piece of evidence in favour of a formula \(\varphi\), denoted \(t\gg\varphi\). A term of the form \(c_\varphi\) is referred to as a \textit{certificate for \(\varphi\)}, and represents a ``canonical'' piece of evidence in support of \(\varphi\), so \(c_\varphi\gg\varphi\); if \(t\gg\varphi\Rightarrow \psi\) and \(s\gg\varphi\) then \(t\cdot s\gg\psi\); if \(t\gg\varphi\) and \(s\gg\psi\) then \(t+s\gg\varphi\) and \(t+s\gg\psi\); \(\gg\) is the \(\subseteq\)-smallest relation satisfying the previous conditions.NEWLINENEWLINEFinally, and crucially for this…
description: scientific article; zbMATH DE number 6244764