Geometric conditioning
As we have seen in Chapter 4, Section 4.5, various distinct definitions of conditional belief functions have been proposed in the past.
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Fabio Cuzzolin
The Geometry of Uncertainty The Geometry of Imprecise Probabilities
Artificial Intelligence: Foundations, Theory, and Algorithms
Series editors Barry O’Sullivan, Cork, Ireland Michael Wooldridge, Oxford, United Kingdom
More information about this series at http://www.springer.com/series/13900
Fabio Cuzzolin
The Geometry of Uncertainty The Geometry of Imprecise Probabilities
Fabio Cuzzolin Department of Computing & Communication Oxford Brookes University Oxford, UK
ISSN 2365-3051 ISSN 2365-306X (electronic) Artificial Intelligence: Foundations, Theory, and Algorithms ISBN 978-3-030-63152-9 ISBN 978-3-030-63153-6 (eBook) https://doi.org/10.1007/978-3-030-63153-6 © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To my dearest parents Elsa and Albino, whom I owe so much to, my beloved wife Natalia and my beautiful son Leonardo
Preface Uncertainty Uncertainty is of paramount importance in artificial intelligence, applied science, and many other areas of human endeavour. Whilst each and every one of us possesses some intuitive grasp of what uncertainty is, providing a formal definition can prove elusive. Uncertainty can be understood as a lack of information about an issue of interest for a certain agent (e.g., a human decision maker or a machine), a condition of limited knowledge in which it is impossible to exactly describe the state of the world or its future evolution. According to Dennis Lindley [1175]: “ There are some things that you know to be true, and others that you know to be false; yet, despite this extensive knowledge that you have, there remain many things whose truth or falsity is not known to you. We say that you a
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