Probabilistic logic in a coherent setting
type: Item
instance of: scholarly article
title: Probabilistic logic in a coherent setting
zbMATH Open document ID: 1040.03017
author: Giulianella Coletti
author: Romano Scozzafava
published in: Trends in Logic -- Studia Logica Library
publication date: 2003-09-07T00:00:00Z
review text: This book will be most appreciated by readers already familiar with current issues in the interpretation of probabilities. Following de Finetti, probabilities are characterised here as linear mappings over propositions, expressing ``degrees of belief''. Thus there is no Boolean ``event space'' as there is in Kolmogorov probabilities. However, coherence is introduced as the requirement that the space of such ``propositional events'' can be extended to an additive Boolean algebra. So the essential difference is one of interpretation, and this is the main concern of the authors. They are particularly concerned with our understanding of conditional probabilities, with many ``ordinary life'' examples to illustrate their analysis. The ``logic'' of the book title is perhaps misleading. Although there is some discussion of truth-values at various times, the book does not attempt to present formally any logical aspects of this interpretation of probability. Some interesting discussion on 3-valued system for example is evocative but not developed. However, there is much detail, often supplemented by specific examples and a large bibliography is continually invoked. The structure of the book may be frustrating to some, though perhaps suited to very familiar readers. For example, chapters and sections are of very different lengths, and there is an informality that makes information such as formal definitions missing or hard to find. The style is characterised by long sentences, sometimes awkward English and excessive use of brackets. A continual use of bold and italic font increases the readers difficulties. For example, this single sentence about the 2-slit experiment has the authors' formatting, and may or may not help understand quantum theory: ``In the previous example the \textbf{two incompatible experiments are not (so to say) ``mentally'' incompatible} if we argue in terms of the general \textit{meaning} of probability (for example P(A\(|\)S1) is the degree of belief in …
Mathematics Subject Classification ID: 03B48
Mathematics Subject Classification ID: 60A99
Mathematics Subject Classification ID: 03-02
zbMATH DE Number: 1975736
zbMATH Keywords: probabilistic logic
zbMATH Keywords: coherence
zbMATH Keywords: probability
zbMATH Keywords: conditional probability
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1975736