Progress in Computer Science and Applied Logic

Mathematical Logic

Foundations for Information Science

Authors: Li, Wei

  • A research monograph with a textbook style, this book contains a well-structured presentation as well as formal proofs for all theoretical results, complete with illustrations by concrete examples
  • New ideas and methodologies from information science and technology are used to annotate the concepts and theorems of mathematical logic, providing a new angle of view for readers from mathematics and a friendly environment for readers from information science to understand the quintessence of mathematical logic
  • The author’s original work on version sequences, revision calculus, and language environments is coherently integrated into the book, enriching the content and the scope of application of mathematical logic
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About this book

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.

Reviews

From the reviews:

“The book consists of two parts. The first part is written for undergraduate university students of computer science and presents the classical first-order predicate logic with set-theoretical interpretation of its formulas and a symmetrical, well-shaped, and beautiful Gentzen-type axiomatic system which describes identically true … formulas of this logic. … The second part may be used for a course for postgraduate students of information science and includes a definition of versions of a formal theory, version sequences and their limits.” (Alex Nabebin, Zentralblatt MATH, Vol. 1185, 2010)

Table of contents (10 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-7643-9977-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Logic
Book Subtitle
Foundations for Information Science
Authors
Series Title
Progress in Computer Science and Applied Logic
Series Volume
25
Copyright
2010
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-9977-1
DOI
10.1007/978-3-7643-9977-1
Series ISSN
2297-0576
Edition Number
1
Number of Pages
XII, 273
Topics