Quantifiers in Action (eBook)

Preface 7
Contents 9
1 Introduction 12
2 Basic Concepts 17
2.1 From Propositional to First Order Logic 17
2.2 Quantification 18
2.3 More on Quantification 22
2.4 Games 28
2.5 More Semantics 29
3 Generalized Quantifiers 34
3.1 Introduction 34
3.2 Generalized Quantifiers 34
3.3 Another view 39
3.4 Basic Complexity 42
4 Quantifiers 46
4.1 Introduction: GQs in query languages 46
4.2 QLGQ 47
4.3 Safety and Domain Independence 53
4.4 Generalized Quantifiers and SQL 59
5 Implementation and Optimization of Standard GQs 63
5.1 Languages to Define GQs 63
5.2 Translating and Optimizing QLGQ 68
5.3 The Interpreter 68
5.4 Optimization 75
5.5 Application to SQL 77
5.6 Monadic vs. Polyadic Quantification 79
6 Quantifier Prefixes 81
6.1 Introduction 81
6.2 Linear and Non-Linear Prefixes in QLGQ 85
6.3 Cumulation 89
6.4 Branching 90
6.5 Linear Prefixes 93
7 Cooperative Query Answering 98
7.1 Introduction 98
7.2 Cooperative Query Answering 98
7.3 Cooperative Query Answering with QLGQ 101
7.4 Further Research in CQA 112
8 Generalized Quantifiers and Natural Language 114
8.1 Introduction 114
8.2 Question Answering 114
8.3 GQs in Natural Language Analysis 117
8.4 QLGQ in QA 123
8.5 CQA, QA and GQs 127
8.6 Challenges 129
9 Extensions 134
9.1 Datalog-like Languages 134
9.2 Distributed Quantification 141
9.3 Other Data Models 150
10 Conclusion 155
References 157