互逆主义逻辑、数学和它们的应用

Preface

Part 1 Mutually-inversistic logical calculus

Chapter 1 Fundaments of predicate calculus

1.1 Material implication vs. mutually inverse implication

1.2 Formation ofterms and propositions

1.3 Simple-complexcomposition

1.4 Zeroth-level predicate calculus

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

2.1 Mutually inverse special propositions vs. mutually inverse general propositions

2.2 Unary cognitive processes

2.3 Binary cognitive processes

2.4 Man's cognitive route

2.5 Classification ofcognitive processes

2.6 Inductive composition vs. decomposition

2.7 The principle ofinductive composition, the principle ofdecomposition, and the principle of mutual inverseness between inductive composition and decomposition

2.8 Truth tables ofinductive composition and decomposition for the connection operators

2.9 Mutually inverse diagrams for the connection operators

2.10 The principle ofmeaningfulness and meaninglessness duality for the distinguished propositions

Chapter 3 First-level single quasi-predicate calculus

3.1 Meaningless and meaningful first-order single empirical or mathematical connection propositions

3.2 Free and bound first-order single empirical or mathematical connection propostions

3.3 First-levelexplicitinductivecomposition

3.4 First-levelimplicitinductivecomposition

3.5 Contradictorypropositions

3.6 First-leveldecomposition

3.7 Quasi-logicalconnectionpropositions

3.8 The decomposition system offirst-level single quasi-predicate calculus

Chapter 4 Second-level single quasi-predicate calculus

4.1 Meaningless and meaningful second-order single logical connection propositions

4.2 Free and bound second-order single logical connection propositions

4.3 Second-levelexplicitinductivecomposition

4.4 Second-levelimplicitinductivecomposition

4.5 Second-leveldecomposition

4.6 Quasi-transcendentlogicalconnectionpropositions

4.7 Knowledge-cognitionscience

4.8 The decomposition system of second-level single quasi-predicate calculus

Chapter 5 First-level multiple predicate calculus

5.1 Property fact proposition segments vs. non-property fact propositions

5.2 Mutually inverse multiple diagrams

5.3 Success diagrams vs. failure diagrams

5.4 Least success diagrams

5.5 Proposition chains and property proposition segment chains

5.6 Multiple empirical or mathematical connection propositions

5.7 Meaningful and bound multiple empirical or mathematical connection propositions

5.8 Mutually inverse multiple diagrams for multiple empmcal or mathematical connection propositions

5.9 Proposition chains, property proposition segment chains, and least success diagrams of multiple empirical or mathematical connection propositions

2.10 Decomposition system offirst-levelmultiple 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

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...