Authors:
- Research monograph of textbook style with well-structured presentation and formal proofs for all theoretical results, illustrated 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Computer Science and Applied Logic (PCS, volume 25)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
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)Authors and Affiliations
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State Key Laboratory of Software Development Environment, Beihang University, Beijing, China
Wei Li
Bibliographic Information
Book Title: Mathematical Logic
Book Subtitle: Foundations for Information Science
Authors: Wei Li
Series Title: Progress in Computer Science and Applied Logic
DOI: https://doi.org/10.1007/978-3-7643-9977-1
Publisher: Birkhäuser Basel
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Birkhäuser Basel 2010
eBook ISBN: 978-3-7643-9977-1Published: 26 February 2010
Series ISSN: 2297-0576
Series E-ISSN: 2297-0584
Edition Number: 1
Number of Pages: XII, 273
Topics: Mathematical Logic and Formal Languages, Mathematical Logic and Foundations