Probability Logics Probability-Based Formalization of Uncertain Reas
The aim of this book is to provide an introduction to probability logic-based formalization of uncertain reasoning. The authors' primary interest is mathematical techniques for infinitary probability logics used to obtain results about proof-theoretical a
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lity Logics Probability-Based Formalization of Uncertain Reasoning
Probability Logics
Zoran Ognjanović Miodrag Rašković Zoran Marković •
Probability Logics Probability-Based Formalization of Uncertain Reasoning
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Zoran Ognjanović Mathematical Institute of the Serbian Academy of Sciences and Arts Belgrade Serbia
Zoran Marković Mathematical Institute of the Serbian Academy of Sciences and Arts Belgrade Serbia
Miodrag Rašković Mathematical Institute of the Serbian Academy of Sciences and Arts Belgrade Serbia
ISBN 978-3-319-47011-5 DOI 10.1007/978-3-319-47012-2
ISBN 978-3-319-47012-2
(eBook)
Library of Congress Control Number: 2016953324 © Springer International Publishing AG 2016 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
The problems of representing, and working with, uncertain knowledge are ancient problems dating, at least, from Leibnitz, and later explored by a number of distinguished scholars—Jacob Bernoulli, Abraham de Moivre, Thomas Bayes, Johann Heinrich Lambert, Pierre-Simon Laplace, Bernard Bolzano, Augustus De Morgan, George Boole, just to name a few of them. In the last decades there is a growing interest in the field connected with applications to computer science and artificial intelligence. Researchers from those areas have studied uncertain reasoning using different tools, and have used many methods for reasoning about uncertainty: Bayesian network, non-monotonic logic, Dempster–Shafer Theory, possibilistic logic, rule-based expert systems with certainty factors, argumentation systems, etc. Some of the proposed formalisms for handling uncertain knowledge are based on probability logics. The present book grew out a sequence of papers on probability logics written by the authors since 1985. Also, some of our papers, from 2
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