
Decidability of Logical Theories and Their Combination
Birkhäuser (Publisher)
Published on 22. October 2021
Book
Paperback/Softback
XIII, 178 pages
978-3-030-56556-5 (ISBN)
Description
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.
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.
More details
Product info
Book
Series
Edition
1st ed. 2020
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
69 s/w Abbildungen, 1 farbige Abbildung
XIII, 178 p. 70 illus., 1 illus. in color.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Weight
363 gr
ISBN-13
978-3-030-56556-5 (9783030565565)
DOI
10.1007/978-3-030-56554-1
Schweitzer Classification
Other editions
Additional editions

João Rasga | Cristina Sernadas
Decidability of Logical Theories and Their Combination
Book
10/2020
Birkhäuser
€64.19
Shipment within 7-9 days
Persons
João Rasga is an Associate Professor and Cristina Sernadas is a Full Professor at the Mathematics Department of Instituto Superior Técnico
Content
Chapter 1: First Order Logic.- Chapter 2: Reasoning with Theories.- Chapter 3: Decidability Results on Theories.- Chapter 4: Quantifier Elimination.- Chapter 5: Combination of Theories.- Appendix: Basics of Computability.- Bibliography.- Table of Symbols.- Subject Index.