Combination of Theories
The objective of the chapter is to discuss decidability of combination of theories sharing only equality. We start by relating the decidability problem with the satisfiability problem in the context of a theory. This relationship is relevant since we prov
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João Rasga Cristina Sernadas
Decidability of Logical Theories and Their Combination
Studies in Universal Logic Series Editor Jean-Yves Béziau (Federal University of Rio de Janeiro, Rio de Janeiro, Brazil) Editorial Board Hajnal Andréka (Hungarian Academy of Sciences, Budapest, Hungary) Mark Burgin (University of California, Los Angeles, CA, USA) Răzvan Diaconescu (Romanian Academy, Bucharest, Romania) Andreas Herzig (University Paul Sabatier, Toulouse, France) Arnold Koslow (City University of New York, New York, USA) Jui-Lin Lee (National Formosa University, Huwei Township, Taiwan) Larissa Maksimova (Russian Academy of Sciences, Novosibirsk, Russia) Grzegorz Malinowski (University of Lódz, Lódz, Poland) Francesco Paoli (University of Cagliari, Cagliari, Italy) Darko Sarenac (Colorado State University, Fort Collins, USA) Peter Schröder-Heister (University of Tübingen, Tübingen, Germany) Vladimir Vasyukov (Russian Academy of Sciences, Moscow, Russia)
This series is devoted to the universal approach to logic and the development of a general theory of logics. It covers topics such as global set-ups for fundamental theorems of logic and frameworks for the study of logics, in particular logical matrices, Kripke structures, combination of logics, categorical logic, abstract proof theory, consequence operators, and algebraic logic. It includes also books with historical and philosophical discussions about the nature and scope of logic. Three types of books will appear in the series: graduate textbooks, research monographs, and volumes with contributed papers.
More information about this series at http://www.springer.com/series/7391
João Rasga Cristina Sernadas •
Decidability of Logical Theories and Their Combination
João Rasga Department of Mathematics Instituto Superior Técnico, Universidade de Lisboa and Instituto de Telecomunicações Lisboa, Portugal
Cristina Sernadas Department of Mathematics Instituto Superior Técnico, Universidade de Lisboa and Instituto de Telecomunicações Lisboa, Portugal
ISSN 2297-0282 ISSN 2297-0290 (electronic) Studies in Universal Logic ISBN 978-3-030-56553-4 ISBN 978-3-030-56554-1 (eBook) https://doi.org/10.1007/978-3-030-56554-1 Mathematics Subject Classification: 03B10, 03B25, 03B62 © Springer Nature Switzerland AG 2020 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 th
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