# Mathematical Logic

## Foundations for Information Science

• Wei Li
Book

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

1. Front Matter
Pages i-xii
2. Wei Li
Pages 1-18
3. Wei Li
Pages 19-44
4. Wei Li
Pages 45-70
5. Wei Li
Pages 71-96
6. Wei Li
Pages 97-116
7. Wei Li
Pages 117-137
8. Wei Li
Pages 139-167
9. Wei Li
Pages 169-185
10. Wei Li
Pages 187-208
11. Wei Li
Pages 209-228
12. Back Matter
Pages 229-261

### 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.

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

Arithmetic Gödel theorem Lemma calculus first-order language forcing formal calculus inference system language environment logic mathematical logic model theory proof proof theory revision calculus

#### Authors and affiliations

• Wei Li
• 1
1. 1.State Key Laboratory of Software Development EnvironmentBeihang UniversityBeijingChina

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-7643-9977-1
• Copyright Information Birkhäuser Basel 2010
• Publisher Name Birkhäuser Basel
• eBook Packages Computer Science
• Print ISBN 978-3-7643-9976-4
• Online ISBN 978-3-7643-9977-1