Overview
- A research monograph with a textbook style, well-structured and providing concrete illustrative examples as well as formal proofs for all theoretical results
- New ideas and methodologies from information science and technology are used to annotate the concepts and theorems of mathematical logic
- Provides a new angle of view for mathematicians and a friendly environment for information scientists 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
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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Elements of Mathematical Logic
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Front Matter
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Logical Framework of Scientific Discovery
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Front Matter
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Back Matter
Keywords
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.
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 inrelevant disciplines.
Authors and Affiliations
About the author
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/10.1007/978-3-0348-0862-0
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2014
Hardcover ISBN: 978-3-0348-0861-3Published: 24 November 2014
eBook ISBN: 978-3-0348-0862-0Published: 07 November 2014
Series ISSN: 2297-0576
Series E-ISSN: 2297-0584
Edition Number: 2
Number of Pages: XIV, 301
Number of Illustrations: 13 b/w illustrations
Topics: Mathematical Logic and Formal Languages, Mathematical Logic and Foundations