周训伟编著的《互逆主义逻辑数学和它们的应用》内容介绍：Since then, I have been constructing mutually-inversistic mathematical logic. Now, itis fully fledged. It includes mutually-inversistic logic, mutually-inversistic mathematics,and their applications. Mutually-inversistic logic includes two calculi and four theoriesof mutual-inversism, mutually-inversistic granular computing, unified logics. Mutually-inversistic mathematics includes mutually-inversistic analytic geometry, mutually-inversistic mathematical analysis, mutually-inversistic abstract algebra, universal matrix.Applications include logic programming (see Part 4), automated theorem proving, planningand scheduling, database, semantic network, expert system, program verification, naturallanguage processing, hardware verification, machine learning, data mining, data warehouse,program refinement, many-valued computer, modern control theory, etc...

Preface

Part 1 Mutually-inversistic logical calculus

 Chapter 1 Fundaments of predicate calculus

 Chapter 2 Human cognitive processes and basic principles of mutually-inversistic logic

 Chapter 3 First-level single quasi-predicate calculus

 Chapter 4 Second-level single quasi-predicate calculus

 Chapter 5 First-level multiple predicate calculus

 Chapter 6 Second-level multiple predicate calculus

 Chapter 7 Mutually-inversistic propositional calculus

Part 2 Mutually-inversistic set theory

 Chapter 8 Fundamentals of mutually-inversistic set theory

 Chapter 9 The Main

 Chapter 10 The auxiliary

Part 3 Mutually-inversistic proof theory vs mutually-inversistic model theory

 Chapter 11 Proof theory vs model theory

 Chapter 12 Mutually-inversistic proof theory

 Chapter 13 Mutually-inversistic model theory

Part 4 Mutually-inversistic recursion theory

 Chapter 14 Mutually-inversistic recursion theory

Part 5 Mutually-inversistic granular computing

 Chapter 15 Mutually-inversistic fuzzy logic based granular computing

 Chapter 16 Mutually-inversistic rough set based granular computing

 Chapter 17 Unified logics

Part 7 Mutually-inversistic analytic geometry

 Chapter 18 Mutually-inversistic analytic geometry

Part 8 Mutually-inversistic mathematical analysis

 Chapter 19 Double-sided discrete calculus

 Chapter 20 Single-sided discrete calculus

 Chapter 21 Unified calculus

Part 9 Mutually-inversistic abstract algebra

 Chapter 22 Auxiliary algebras

 Chapter 23 Main-auxiliary algebras

Part 10 Universal matrices

 Chapter 24 Universal matrices

Part 11 Applications of decomposition

 Chapter 25 Inference rule systems vs mutually-inversistic automated decomposition systems

 Chapter 26 Mutually-inversistic relational databases

 Chapter 27 Mutually-inversistic planning and scheduling

 Chapter 28 Mutually-Inversistic Semantic Network

 Chapter 29 Mutually-inversistic expert systems

 Chapter 30 Transformation of second-level inference rule systems into second-level automated decomposition systems

 Chapter 31 Applications of First-Level Hypothetical Inference

 Chapter 32 Axiomatic systems brought into mutually-inversistic automated decomposition systems

Part 12 Applications of implicit inductive compositions

 Chapter 33 Applications of implicit inductive compositions

Part 13 Applications of explicit inductive composition

 Chapter 34 Mutually-inversistic machine learning

 Chapter 35 Multiple connection operators association rule mining

 Chapter 36 Mutually-inversistic program refinement

Part 14 Applications ofmutually-inversistic mathematics

 Chapter 37 Applications of universal matrix

 Chapter 38 Mutually-inversistic many-valued computer

 Chapter 39 Applications of mutually-inversistic mathematical analysis

References