Mathematical Logic
Foundations for Information Science
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 firstorder 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 metalanguage 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.
less266 pages; ISBN 9783764399771
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Title: Mathematical Logic
Author: Wei Li
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 Academic > Mathematics > General > Logic, Symbolic and mathematical
 Academic > Mathematics > Instruments and machines
 Academic > Mathematics > Calculus
 Academic > Mathematics > Analytic mechanics
 Academic > Logic > Mathematics; Philosophy
 Academic > Computer Science
 Mathematics > Logic
 Computers > Mathematical & Statistical Software
In the press
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 firstorder predicate logic with settheoretical interpretation of its formulas and a symmetrical, wellshaped, and beautiful Gentzentype 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)