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半线性子结构逻辑的标准完备性(英文) 版权信息
- ISBN:9787030668769
- 条形码:9787030668769 ; 978-7-03-066876-9
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 所属分类:>
半线性子结构逻辑的标准完备性(英文) 内容简介
本书系统阐述模糊逻辑标准完备性证明的各种方法和理论,为初学者尽可能多的提供理论和技术上的细节,使其能尽快进入这一课题的研究工作。特别地,较为详细的介绍了作者在这些方面所做的工作,对IUL完备性的证明进行了详细的论述,并针对主算法的很困难部分给出了实例,这在一般地论文写作是不可能的。
半线性子结构逻辑的标准完备性(英文) 目录
Contents
Preface
Chapter 1 Introduction 1
1.1 Overview of the standard completeness for fuzzy logics 1
1.2 Standard completeness of IUL 2
1.3 My work on the standard completeness for IUL and reviewers'comments on it 3
1.3.1 Reviewers'comments in 2015 by APAL 3
1.3.2 Reviewers'comments in 2016 by FSS 5
1.3.3 Reviewers'comments in 2018 by FSS 7
1.3.4 Reviewers'comments in 2018 on my second paper by JSL 9
1.3.5 Communication with editors and colleagues 10
Chapter 2 The Logic HpsUL* and Its Chain Completeness 12
2.1 The logic HpsUL* 12
2.2 Proof by cases property and prelinearity property of HpsUL 22
2.3 The chain completeness for HpsUL 27
2.4 Extensions of HpsUL 31
Chapter 3 Jenei and Montagna's Algebraic Method 38
3.1 The logic MTL and MTL-algebras 38
3.2 Standard completeness for MTL 40
3.3 Standard completeness for IMTL 47
Chapter 4 Wang's Constructions on HpsUL*-Chains 52
4.1 New extensions of HpsUL* and new algebras 52
4.2 Structures X on HpsUL*-chains 55
4.3 Standard completeness for CnIUL and IULw 62
4.4 A proof of associativity of in X for IUL 71
Chapter 5 Metcalfe and Montagna's Proof-Theoretic Method 95
5.1 Standard completeness and the density rule 95
5.2 Hypersequent calculi 106
5.3 Cut-elimination 112
5.4 Density elimination 117
Chapter 6 Wang's Proof-Theoretic Method 132
6.1 Introduction 132
6.2 Proof of the Main theorem: A computational example 133
6.3 Preprocessing of proof tree 143
6.4 The generalized density rule (D) for GL 152
6.5 Extraction of elimination rules 158
Chapter 7 Standard Completeness for IUL 166
7.1 Separation of one branch 166
7.2 Separation algorithm of multiple branches 172
7.3 The proof of Main theorem 187
7.4 Final remarks and open problems 189
Chapter 8 An Extension of Wang's Proof-Theoretic Method 190
8.1 Introduction 190
8.2 GpsUL** and its cut-elimination 192
8.3 GpsUL and its generalized density rule (D) 202
8.4 Density elimination for GpsUL* 216
Chapter 9 Two Big Examples for Separation Algorithms 224
9.1 Proof of Theorem 7.2.2: A big example 224
9.1.1 Preprocessing of proof tree 225
9.1.2 Elimination rules 227
9.1.3 Separation of one branch 228
9.1.4 Separations of two branches 230
9.1.5 A concise algorithm 235
9.1.6 Separation of four branches 237
9.2 Proof of Lemma 8.4.7: A big example 238
9.2.1 Maximal nodes, complete sets and their heights 241
9.2.2 Some copies of can't be contracted in G1(J) 241
9.2.3 Illustration of Lemma 8.4.7: Construct 1;2 246
9.2.4 Remark on construction of 250
9.2.5 Constructing of 251
9.2.6 is undefined and can't be constructed by the new main algorithm 254
Bibliography 256
Preface
Chapter 1 Introduction 1
1.1 Overview of the standard completeness for fuzzy logics 1
1.2 Standard completeness of IUL 2
1.3 My work on the standard completeness for IUL and reviewers'comments on it 3
1.3.1 Reviewers'comments in 2015 by APAL 3
1.3.2 Reviewers'comments in 2016 by FSS 5
1.3.3 Reviewers'comments in 2018 by FSS 7
1.3.4 Reviewers'comments in 2018 on my second paper by JSL 9
1.3.5 Communication with editors and colleagues 10
Chapter 2 The Logic HpsUL* and Its Chain Completeness 12
2.1 The logic HpsUL* 12
2.2 Proof by cases property and prelinearity property of HpsUL 22
2.3 The chain completeness for HpsUL 27
2.4 Extensions of HpsUL 31
Chapter 3 Jenei and Montagna's Algebraic Method 38
3.1 The logic MTL and MTL-algebras 38
3.2 Standard completeness for MTL 40
3.3 Standard completeness for IMTL 47
Chapter 4 Wang's Constructions on HpsUL*-Chains 52
4.1 New extensions of HpsUL* and new algebras 52
4.2 Structures X on HpsUL*-chains 55
4.3 Standard completeness for CnIUL and IULw 62
4.4 A proof of associativity of in X for IUL 71
Chapter 5 Metcalfe and Montagna's Proof-Theoretic Method 95
5.1 Standard completeness and the density rule 95
5.2 Hypersequent calculi 106
5.3 Cut-elimination 112
5.4 Density elimination 117
Chapter 6 Wang's Proof-Theoretic Method 132
6.1 Introduction 132
6.2 Proof of the Main theorem: A computational example 133
6.3 Preprocessing of proof tree 143
6.4 The generalized density rule (D) for GL 152
6.5 Extraction of elimination rules 158
Chapter 7 Standard Completeness for IUL 166
7.1 Separation of one branch 166
7.2 Separation algorithm of multiple branches 172
7.3 The proof of Main theorem 187
7.4 Final remarks and open problems 189
Chapter 8 An Extension of Wang's Proof-Theoretic Method 190
8.1 Introduction 190
8.2 GpsUL** and its cut-elimination 192
8.3 GpsUL and its generalized density rule (D) 202
8.4 Density elimination for GpsUL* 216
Chapter 9 Two Big Examples for Separation Algorithms 224
9.1 Proof of Theorem 7.2.2: A big example 224
9.1.1 Preprocessing of proof tree 225
9.1.2 Elimination rules 227
9.1.3 Separation of one branch 228
9.1.4 Separations of two branches 230
9.1.5 A concise algorithm 235
9.1.6 Separation of four branches 237
9.2 Proof of Lemma 8.4.7: A big example 238
9.2.1 Maximal nodes, complete sets and their heights 241
9.2.2 Some copies of can't be contracted in G1(J) 241
9.2.3 Illustration of Lemma 8.4.7: Construct 1;2 246
9.2.4 Remark on construction of 250
9.2.5 Constructing of 251
9.2.6 is undefined and can't be constructed by the new main algorithm 254
Bibliography 256
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