Studies in Universal Logic

Decidability of Logical Theories and Their Combination

Authors: Rasga, João, Sernadas, Cristina

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  • Provides a comprehensive, self-contained introduction to decidability of first-order theories, using detailed proofs and examples to illustrate and clarify complex concepts
  • Incorporates computability theory and reduction techniques to determine the decidability of theories
  • Illustrates a variety of ways to deduce logical consequences from a theory, including the use of Gentzen calculus for first-order logic
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eBook $54.99
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  • ISBN 978-3-030-56554-1
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About this Textbook

This textbook provides a self-contained introduction to decidability of first-order theories and their combination. The technical material is presented in a systematic and universal way and illustrated with plenty of examples and a range of proposed exercises.
After an overview of basic first-order logic concepts, the authors discuss some model-theoretic notions like embeddings, diagrams, and elementary substructures. The text then goes on to explore an applicable way to deduce logical consequences from a given theory and presents sufficient conditions for a theory to be decidable. The chapters that follow focus on quantifier elimination, decidability of the combination of first-order theories and the basics of computability theory. 
The inclusion of a chapter on Gentzen calculus, cut elimination, and Craig interpolation, as well as a chapter on combination of theories and preservation of decidability, help to set this volume apart from similar books in the field.
Decidability of Logical Theories and their Combination is ideal for graduate students of Mathematics and is equally suitable for Computer Science, Philosophy and Physics students who are interested in gaining a deeper understanding of the subject. The book is also directed to researchers that intend to get acquainted with first-order theories and their combination.

About the authors

João Rasga is an Associate Professor and Cristina Sernadas is a Full Professor at the Mathematics Department of Instituto Superior Técnico

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $54.99
price for Mexico
  • ISBN 978-3-030-56554-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase Institutional customers should get in touch with their account manager
Hardcover $69.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
Decidability of Logical Theories and Their Combination
Authors
Series Title
Studies in Universal Logic
Copyright
2020
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-56554-1
DOI
10.1007/978-3-030-56554-1
Hardcover ISBN
978-3-030-56553-4
Series ISSN
2297-0282
Edition Number
1
Number of Pages
XIII, 178
Number of Illustrations
69 b/w illustrations, 1 illustrations in colour
Topics