# Mathematical Logic

## Foundations for Information Science

Textbook

Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 25)

1. Front Matter
Pages i-xiv
2. ### Elements of Mathematical Logic

1. Front Matter
Pages 1-1
2. Wei Li
Pages 3-21
3. Wei Li
Pages 23-53
4. Wei Li
Pages 55-81
5. Wei Li
Pages 83-115
6. Wei Li
Pages 117-136
3. ### Logical Framework of Scientific Discovery

1. Front Matter
Pages 137-137
2. Wei Li
Pages 139-160
3. Wei Li
Pages 161-215
4. Wei Li
Pages 217-233
5. Wei Li
Pages 235-255
6. Wei Li
Pages 257-278
4. Back Matter
Pages 279-301

### Introduction

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.

The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging.

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.

### Keywords

Gödel theorem first-order language inductive inference language environment revision calculus version sequence

#### Authors and affiliations

1. 1.School of Computer Science & EngineeringBeihang University State Key Lab. SoftwareBeijingChina

#### About the authors

Wei Li is Professor at the School of Computer Science and Engineering and Director of the National Laboratory of Software Development Environment at Beihang University in Beijing, China.

### Bibliographic information

• Book Title Mathematical Logic
• Book Subtitle Foundations for Information Science
• Authors Wei Li
• Series Title Progress in Computer Science and Applied Logic
• Series Abbreviated Title Progress Computer Science(Birkhäuser)
• DOI https://doi.org/10.1007/978-3-0348-0862-0
• Copyright Information Springer Basel 2014
• Publisher Name Birkhäuser, Basel
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-3-0348-0861-3
• eBook ISBN 978-3-0348-0862-0
• Series ISSN 2297-0576
• Series E-ISSN 2297-0584
• Edition Number 2
• Number of Pages XIV, 301
• Number of Illustrations 13 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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