Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science
This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. Th
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Janusz Czelakowski Editor
Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science
Outstanding Contributions to Logic Volume 16
Editor-in-chief Sven Ove Hansson, Royal Institute of Technology, Stockholm, Sweden Editorial Board Marcus Kracht, Universität Bielefeld Lawrence Moss, Indiana University Sonja Smets, Universiteit van Amsterdam Heinrich Wansing, Ruhr-Universität Bochum
More information about this series at http://www.springer.com/series/10033
Janusz Czelakowski Editor
Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science
123
Editor Janusz Czelakowski Institute of Mathematics and Informatics University of Opole Opole Poland
ISSN 2211-2758 ISSN 2211-2766 (electronic) Outstanding Contributions to Logic ISBN 978-3-319-74771-2 ISBN 978-3-319-74772-9 (eBook) https://doi.org/10.1007/978-3-319-74772-9 Library of Congress Control Number: 2017964448 © Springer International Publishing AG 2018 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. 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
Ad multos annos, Don!
Preface
1. In a most surprising way logic is connected with algebra. Each language, whether natural or artificial, possesses a complex algebraic structure. In the simplest case this structure is revealed in the languages of propositional logics as certain absolutely free algebras. The above linguistic perspective establishes the first bridge between logic and algebra. There are more links between these two domains and they exist on a deeper level. George Boole (1854) proved that the “laws of thought” can be framed algebraically as identities of an algebra. Thus, thinking is also “algebraizable”. Boole’s work was extended in
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