A New Perspective on Nonmonotonic Logics
"Logics are like shadows on a wall; to understand why they dance as they do, and how they can be made to move differently, one needs to look at the mathematical structures from which they can be projected. That is a methodology that has long proven its va
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ew Perspective on Nonmonotonic Logics
A New Perspective on Nonmonotonic Logics
Dov M. Gabbay Karl Schlechta •
A New Perspective on Nonmonotonic Logics
123
Dov M. Gabbay Department of Computer Science King’s College London London UK
Karl Schlechta CNRS, LIF UMR 7279 Aix-Marseille Université Marseille France
and
and
Department of Computer Science Bar-Ilan University Ramat-Gan Israel
Frammersbach Germany
and Computer Science and Communications, Faculty of Sciences Université de Luxembourg Esch-sur-Alzette Luxembourg
ISBN 978-3-319-46815-0 DOI 10.1007/978-3-319-46817-4
ISBN 978-3-319-46817-4
(eBook)
Library of Congress Control Number: 2016952896 © 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
Contents
Part I 1
Introduction
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Purpose and Organisation of the Book . . . . . . . . 1.1.2 Concise Overview . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Nonmonotonic Logics . . . . . . . . . . . . . . . . . . . . . 1.1.4 Basic Definitions - Chapter 2 . . . . . . . . . . . . . . . 1.1.5 Inheritance Systems - Chapter 3 . . . . . . . . . . . . . 1.1.6 Reiter Defaults - Chapter 4 . . . . . . . . . . . . . . . . . 1.1.7 Preferential Structures - Chapter 5 . . . . . . . . . . . . 1.1.8 Algebraic and Structural Semantics . . . . . . . . . . . 1.1.9 Deontic Logic - Chapter 6 . . . . . . . . . . . . . . . . . . 1.1.10 Theory Revision, Update and Counterfactuals: Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.11 Neurology - Chapter 8 . . . . . . . . . . . . . . . . . . . . . 1.1.12 Interpolation - Cha
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