Public and private communication are different: Results on relative expressivity
type: Item
instance of: scholarly article
title: Public and private communication are different: Results on relative expressivity
zbMATH Open document ID: 1195.03023
author: Bryan Renne
published in: Synthese
publication date: 2009-06-16T00:00:00Z
review text: There are few expressivity results in dynamic epistemic logic. This publication contains such results and is therefore a welcome addition to the literature. What is the point of expressivity? In logic, there is an intimate relation between relational structures and languages used to describe properties of these structures. Some languages can describe more properties than others. We can measure this as follows. Imagine having two different structures. If there is a formula in one of these languages that is true in one structure and false in the other structure, but there is no such formula in the other language, then we conclude that the first language is more expressive than the other language: it is able to `express' a structural difference that cannot be expressed in the other language. Now it may well be that there are yet other structures with a difference that can be expressed in the second but not in the first language: being more expressive is not a total order. Familiar with this structural way to explain expressivity, it surprised us to see Renne define expressivity by way of embedding languages into one another: a language is more expressive than another one if there is an (inductively defined) translation from the latter into the former such that every formula is translated to a logically equivalent formula. But this way of viewing expressivity indeed amounts to the same. In Renne's setting the structures are \textit{pointed multi-agent Kripke models} and the languages are languages of so-called \textit{dynamic epistemic logics}: they contain \textit{epistemic} modal operators modelling belief or knowledge, they may also contain \textit{infinitary epistemic} modal operators (interpreted as fixpoints) standing for common knowledge (or common belief), and they contain \textit{dynamic} modal operators modelling change of belief or knowledge. So, for example, \(K_i p\) stands for `agent \(i\) knows that \(p\)', \(C_{ij} p\) stands for `agents \(i\) and \(j\) …
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 5565232
zbMATH Keywords: dynamic epistemic logic
zbMATH Keywords: expressivity
zbMATH Keywords: private communication
zbMATH Keywords: public communication
zbMATH Keywords: public announcement
MaRDI profile type: Publication
full work available at URL: s11229-008-9395-6
OpenAlex ID: W2015764012
cites work: Logics for epistemic programs
cites work: The Logic of Public Announcements, Common Knowledge, and Private Suspicions
cites work: Modal logic
cites work: Q4845472
cites work: Reasoning about information change
cites work: Epistemology Without Knowledge and Without Belief
cites work: A completeness theorem in modal logic
cites work: Logics of public communications
cites work: Logics of communication and change
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DOI: 10.1007/S11229-008-9395-6
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description: scientific article; zbMATH DE number 5565232