吴士珑的BLOG(Shilong Wu)

Concept Algebra (Book)

General Comment of Concept Algebra

--Same Foundation of Logic and Set

Part One Concept Algebra

Overview of Concept Algebra

Chapter 1 Definition of Concept Algebra

1.1      Definition of Axioms on Concept Algebra

1.2      Operations on Concept Algebra

1.3      Concept Expression and Proposition

1.4      Conversion among Compound Operations

1.5      Equivalent Expression of Compound Operations

1.6      “Affirmative Law Theorem” and Reasonable Constant υ

1.7      “Negative Law Theorem”

1.8      Axioms of Boolean Algebra got from Concept Algebra

Chapter 2 Equation Transformation Rules on Concept Algebra

2.1   Overview about Equation Transformation Rules

2.2   Proof of Equation Transformation Rules

2.3   Basic Models of Concept Equation

2.4   Equation Transformation Rules of Compound Operations

2.5   Proof of Equation Transformation Rules of Compound Operations

Chapter 3 Simplification of Concept Expression

  3.1 Overview of Concept Expression Simplification and Basic Formula for Simplifying

  3.2 Basic Simplification Formula Proving

  3.3 Simplification of Concept Expression

Chapter 4 Operation of Concept Expressions

  4.1 Proof of Concept Expression Equality

  4.2 Concept Laws Proving

Chapter 5 Foundation of Solving Concept Equation

  5.1 Solving Concept Equation of General Form

  5.2 Normal Model of Concept Equation

  5.3 Least Solution Theorem and Most Solution Theorem in Normal Equation

  5.4 Solving Concept Equation in Normal Model

Chapter 6 Compound Operation Theorems of Concept

  6.1 Overview of Compound Operation Theorems of Concept

  6.2 Proving Compound Operation Theorems of Concept

Chapter 7 Concept Equation of Compound Operation

  7.1 Overview

  7.2 Solving Concept Equation of no same variable

  7.3 Solving Concept Equation Composed of Premises of Hegel’s Law

7.4 Solving Concept Equation Composed of Premises of Affirmative Negation law

7.5 Solving Concept Equation Composed of One Premise and Conclusion of Affirmative Negation law

7.6 Solving Concept Equation composed of One Premise and Conclusion of Affirmative Affirmation law

7.7 Solving Concept Equation Composed of One Premise and Conclusion of Negative Negation law

Chapter 8 Deduction of Concept Laws Using Compound Operation

  8.1 Overview of Concept Laws

  8.2 Elucidation of Concept Laws

  8.3 Proof of Concept Laws Using Compound Operation

Chapter 9 Calculation of Concept

  9.1 Overview

  9.2 Calculation of One Concept Expression

  9.3 Calculating Instance of One Concept Expression

  9.4 Kinds of Multiple Concept Expressions

  9.5 Calculation of Two Independent Concept Expressions

  9.6 Instance of Calculation of Two Independent Concept Expressions

  9.7 Calculation of Multiple Independent Concept Expressions

  9.8 Calculation of Related Concept Expressions

  9.9 New Affirmation Calculated from Known Propositions

Part Two Set Algebra

Overview of Set Algebra

Chapter 1 Definition of Set Algebra

1.1   Definition of Set Algebra

1.2   Explanation of Operations

1.3   Conversion of Compound Operations

1.4   Equivalent Expression of Compound Operations

1.5    Proof of Equivalent Expression

1.6   Affirmative Law Theorem and Reasonable Constant υ

1.7   Negative Law Theorem

1.8   Axioms of Classical Set Theory Got From Set Algebra

Chapter 2 Equation Transformation Rules on Set Algebra

  2.1 Overview of Equation Transformation Rules on Set Algebra

  2.2 Proving Equation Transformation Rules on Set Algebra

  2.3 Basic Model of Set Equation

  2.4 Equation Transformation Rules of Compound Operations

 2.5 Proving Compound Equation Transformation Rules

Chapter 3 Simplification of Set Expression

  3.1 Overview of Simplification of Set Expression

  3.2 Proving Basic Formula of Simplification

  3.3 Examples of Simplification of Set Expressions

Chapter 4 Operation of Set Equation

  4.1 Proving Equality of Set Expression

  4.2 Proving Set Laws

Chapter 5 Solving Base of Set Equation

  5.1 Solving Method of Set Equation in General Form

  5.2 Normal Form of Set Equation

  5.3 Least Solution Theorem and Most Solution Theorem in Normal Equation

  5.4 Solving Normal Form of Set Equation

Chapter 6 Set Theorems of Compound Operations

  6.1 Overview of Set Theorems of Compound Operations

  6.2 Proving Set Theorems of Compound Operations

Chapter 7 Set Equations of Compound Operations

  7.1 Overview

  7.2 Solving Set Equation of no same variable

  7.3 Solving Set Equation Constituted by Premises of Set Complementary Complement law

7.4 Solving Set Equation Constituted by Premises of Equal Complement law

7.5 Solving Set Equation Constituted by One Premise and Conclusion of Set Equal Complement law

7.6 Solving Set Equation Constituted by One Premise and Conclusion of Set Equal Transferring law

7.7 Solving Set Equation Constituted by One Premise and Conclusion of Set Complementary Complement law

Chapter 8 Deduction of Set Laws Using Compound Operation

8.1 Overview of Set Laws

8.2 Explanation of Set Laws

8.3 Proving Set Laws Using Compound Operation

Part Three Logic Algebra

Overview of Logic Algebra 

 Chapter 1 Definition of Logic Algebra

1.1    Definition of Logic Algebra

1.2    Operations Explanation of Logic Algebra

1.3    Conversion among Compound Operations

1.4   Concept Expression and Proposition

1.5    Equivalent Expression of Compound Operation

1.6 Affirmative Law Theorem and Reasonable Constant υ

1.7 Negative Law Theorem

1.8 Axioms of Boolean algebra got from Logic Algebra

Chapter 2 Basic Operation Rules on Logic Algebra

  2.1 Overview of Basic Operation Rules on Logic Algebra

  2.2 Proving Basic Operation Rules on Logic algebra

  2.3 Basic Model of Logic Equation

  2.4 Equation Transformation Rules of Compound Operations

  2.5 Proving Equation Transformation Rules of Compound Operation

Chapter 3 Simplification of Logic Expression

  3.1 Overview of Logic Expression Simplification and Basic Simplification Formula

  3.2 Proving Basic Formula of Simplification

  3.3 Examples of Simplification of Logic Expression

Chapter 4 Operation of Logic Equation

  4.1 Proving Equality of Logic Expression

  4.2 Proving Logic Laws

Chapter 5 Solution Base of Logic Equation

  5.1 Solution Method of Logic Equation in General Form

  5.2 Normal Form of Logic Equation

  5.3 Minimum Solution Theorem and Maximum Solution Theorem in Logic Normal Equation

  5.4 Solving Normal Form of Logic Equation

Chapter 6 Logic Theorems of Compound Operations

  6.1 Overview of Logic Theorems of Compound Operations

  6.2 Proving Logic Theorems of Compound Operations

Chapter 7 Logic Equation of Compound Operations

  7.1 Overview

  7.2 Solving Logic Equation of No Same Variable

  7.3 Solving Logic Equation Constituted by Premises of Hegel’s Law

7.4 Solving Logic Equation Constituted by Premises of Affirmative Negation law

7.5 Solving Logic Equation Constituted by One Premise and Conclusion of Affirmative Negation law

7.6 Solving Logic Equation Constituted by One Premise and Conclusion of Affirmative Affirmation law

7.7 Solving Logic Equation Constituted by One Premise and Conclusion of Negative Negation law

Chapter 8 Deduction of Logic Laws Using Compound Operation

8.1 Overview of Logic Laws

8.2 Explanation of Logic Laws

8.3 Proving Logic Laws Using Compound Operation