Decidability of Logical Theories and Their Combination. 1st ed. 2020

種類:

電子ブック

責任表示:

by João Rasga, Cristina Sernadas

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2020

著者名:

• Rasga, João.
• Sernadas, Cristina.
• SpringerLink (Online service)

シリーズ名:

Studies in Universal Logic ;

ISBN:

9783030565541 [3030565548]    

注記:

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.
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 Com

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