Mathematical Logic: Foundations for Information Science: 25 (Progress in Computer Science and Applied Logic) - Hardcover

Li, Wei

Hardcover

ISBN 10: 3764399767 ISBN 13: 9783764399764

Publisher: Birkhauser Verlag AG, 2009

Synopsis

Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. It provides guidelines for the development of information science and technology. This book, with 10 chapters, presents basic principles and formal calculus of mathematical logic systematically. The first five chapters cover the core contents of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Godel's theorems. The contents of the last five chapters are extensions and developments of classical mathematical logic. This part elaborates version sequences of formal theories and their limits, the system of revision calculus, proxchemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. It also describes the paradigm of environments of three kinds of languages and the basic principles of metalanguage environments and addresses the workflow of scientific research in the information era. The first five chapters of this book may be used as an undergraduate text in mathematical logic and the last five chapters may be taught to graduate students in relevant disciplines. The book may serve as a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences.

About this title

From the Back Cover

Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage.

This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.

Edition details

• Publisher: Birkhauser Verlag AG
• Publication date: 2009
• Language: English
• ISBN 10: 3764399767
• ISBN 13: 9783764399764
• Binding: Hardcover
• Number of pages: 273