Li W. Mathematical Logic Foundations for Information Science

Birkhäuser, 2010. — 272 pp.The book consists of two parts, each containing five chapters. The first part presents the core ideas of classical mathematical logic, while the second part deals with the author’s work on formalizing axiomatization.
The second part includes a definition of versions of a formal theory, version sequences and their limits. It formalizes the revision of formal theories, defines the concept of proscheme, and uses it to describe a methodology for the evolution of formal theories. It goes on to study inductive inference and prescribes the principles of a meta-language environment. These are an extension and development of classical mathematical logic.
This book adopts the rigorous standards of classical mathematical logic: All concepts are strictly defined and illustrated with examples; all theorems are proved and details of proofs are provided if at all possible; all quoted conclusions and methods are referred to their original authors and sources. This book is intended to be a course book for postgraduate students of information science, but the first five chapters may be used as a textbook for undergraduate students.Syntax of First-Order Languages
Models of First-Order Languages
Formal Inference Systems
Computability & Representability
GЁodel Theorems
Sequences of Formal Theories
Revision Calculus
Version Sequences
Inductive Inference
Workflows for Scientific Discovery