| 摘要 | 第1-8页 |
| Abstract | 第8-14页 |
| Chapter 1 Preface | 第14-19页 |
| ·Research Background | 第14页 |
| ·Main Contents,Signincation, Current Research Statuses | 第14-17页 |
| ·Structure of This Paper | 第17-19页 |
| Chapter 2 Preliminaries | 第19-25页 |
| ·Definitions | 第19-23页 |
| ·Theories | 第23-25页 |
| Chapter 3 Duality in Lattice Implication Algebra | 第25-33页 |
| ·Principle of Duality in the Sense of Class | 第25-26页 |
| ·P rinciple of Duality in Lattice Implication Algebra | 第26-28页 |
| ·Dual Operators | 第26页 |
| ·Principle of Duality in Lattice Implication Algebra | 第26-28页 |
| ·Applications of Principle of Duality in Lattice Implication Algebra | 第28-32页 |
| ·Applications in Concepts | 第28-31页 |
| ·Applications in Theorems | 第31-32页 |
| ·Conclusion | 第32-33页 |
| Chapter 4 Perfection of Certain Conclusions on Lattice Implication Algebra | 第33-40页 |
| ·Related Conclusions | 第33页 |
| ·Perfection of Theorem 4.1.1 and Expression 4.1.1 | 第33-34页 |
| ·Proof for Theorem 4.1.1 | 第33-34页 |
| ·Analysis of Expression 4.1.1 | 第34页 |
| ·Perfection of Expression 4.1.2,4.1.3 | 第34-35页 |
| ·Analysis of Exptession 4.1.2 | 第34-35页 |
| ·Analysis of Expression 4.1.3 | 第35页 |
| ·Perfection of the Proof for Expression 4.1.4 | 第35-40页 |
| ·Conclusions Used in the Proof for Expression 4.1.4 | 第35-37页 |
| ·Perfection of Expression 4.1.4 and Its Proof | 第37-38页 |
| ·Proof for Theorem 4.3.3 | 第38-40页 |
| Chapter 5 Dual Atom and Filter Generated by a Boolean Element | 第40-43页 |
| ·Dual Atom | 第40-41页 |
| ·Filter Generated by a Boolean Element | 第41-43页 |
| Chapter 6 On Filters of Lattice Implication Product Algebra | 第43-62页 |
| ·Filters of Lattice Implication Product Algebra L~1×L~2 | 第43-49页 |
| ·Filters of L_m and L_m × L_n | 第49-53页 |
| ·Filters of L_m | 第49-51页 |
| ·Filters of L_m × L_n | 第51-53页 |
| ·Applications | 第53-62页 |
| ·Structures and Filters of Non-chain L_6, L_8 and L_9 | 第53-60页 |
| ·Positions of Non-trivial Filters in L_m × L_n and L_m × L_n×L_k | 第60-61页 |
| ·A Kind of Lattice H Implication Algebra | 第61-62页 |
| Conclusions and Future Works | 第62-64页 |
| Acknowledgements | 第64-65页 |
| Reference | 第65-69页 |
| List of Publications and Research Projects | 第69页 |
