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.
