Mathematical Logic: Foundations for Information Science

✍ Scribed by Wei Li (auth.)

• Publisher: Birkhäuser Basel
• Year: 2014
• Tongue: English
• Leaves: 303
• Series: Progress in Computer Science and Applied Logic 25
• Edition: 2
• Category: Library

✦ Synopsis

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 in relevant disciplines.

✦ Table of Contents

Front Matter....Pages i-xiv
Front Matter....Pages 1-1
Syntax of First-Order Languages....Pages 3-21
Models of First-Order Languages....Pages 23-53
Formal Inference Systems....Pages 55-81
Computability and Representability....Pages 83-115
Gödel Theorems....Pages 117-136
Front Matter....Pages 137-137
Sequences of Formal Theories....Pages 139-160
Revision Calculus....Pages 161-215
Version Sequences....Pages 217-233
Inductive Inference....Pages 235-255
Meta-Language Environments....Pages 257-278
Back Matter....Pages 279-301

✦ Subjects

Mathematical Logic and Formal Languages; Mathematical Logic and Foundations