Mathematical Logic: Foundations for Information Science

by Wei Li

Overview

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.

Product Details

ISBN-13:	9783034808613
Publisher:	Springer Basel
Publication date:	11/08/2014
Series:	Progress in Computer Science and Applied Logic , #25
Edition description:	2nd ed. 2014
Pages:	301
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

About the Author

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.

Table of Contents

Preface.- Preface to the Second Edition.- I Elements of Mathematical Logic.- 1 Syntax of First-Order Languages.- 2 Models of First-Order Languages.- 3 Formal Inference Systems.- 4 Computability & Representability.- 5 Gödel Theorems.- II Logical Framework of Scientific Discovery.- 6 Sequences of Formal Theories.- 7 Revision Calculus.- 8 Version Sequences.- 9 Inductive Inference.- 10 Meta-Language Environments.- Appendix 1 Sets and Maps.- Appendix 2 Proof of the Representability Theorem.- Bibliography.- Index.

Editorial 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)

From the Publisher