Decidability of Logical Theories and Their Combination
Authors: Rasga, João, Sernadas, Cristina
Free Preview- 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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- About this Textbook
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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
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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)
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First-Order Logic
Pages 1-34
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Reasoning with Theories
Pages 35-73
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Decidability Results on Theories
Pages 75-99
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Quantifier Elimination
Pages 101-141
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Combination of Theories
Pages 143-159
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Table of contents (5 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Decidability of Logical Theories and Their Combination
- Authors
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- João Rasga
- Cristina Sernadas
- 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
