## Quantifiers in Action: Generalized Quantification in Query, Logical and Natural LanguagesThe database industry is a multi-billion, world-wide, all-encompassing part of the software world. Quantifiers in Action: Generalized Quantification in Query, Logical and Natural Languages introduces a query language called GQs—Generalized Quantification in Query. Most query languages are simply versions of First Order Logic (FOL). GQs are an extension of the idea of quantifier in FOL. GQs are a perfect example of a practical theory within databases. This book provides a brief background in logic and introduces the concept of GQs, and then develops a query language based on GQs. Using Query Language with Generalized Quantifiers, the reader explores the efficient implementation of the concept, always a primary consideration in databases. This professional book also includes several extensions for use with documents employing question and answer techniques. Designed for practitioners and researchers within the database management field; also suitable for advanced-level students in computer science. |

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### Contents

Generalized Quantiﬁers 25 | 28 |

A Query Language with Generalized Quantiﬁers | 37 |

Implementation and Optimization of Standard GQs | 55 |

6 | 73 |

Cooperative Query Answering 91 | 90 |

Generalized Quantiﬁers and Natural Language | 107 |

Extensions | 127 |

Conclusion | 149 |

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algorithm approach arity assume basic binary relation bound variables called Cartesian product chapter complex compute concept considered context corresponds Datalog deﬁnable deﬁned deﬁnition denote determine diﬀerent diﬃcult domain independent downward monotone eﬀect eﬃcient elements empty answer equivalent evaluated example existential existential quantiﬁer expressive power extended ﬁeld ﬁnd ﬁnite models ﬁrst argument ﬁve ﬁxpoint FOL sentence formal formula free variables function given graph hence Henkin preﬁx iﬀ inﬁnite instance interpretation introduced Intuitively isomorphism Lectures(Peter,crs Lemma linguistic monadic quantiﬁers natural language natural numbers negation node Note optimization outer join parameter predicate preﬁxes prenex normal form problem properties QA system QLGQ query quantiﬁer preﬁxes quantiﬁer Q quantiﬁers of type Query Answering query languages question relational algebra relational algebra expression relax restrict result semantics set of quantiﬁers set term sieve conditions simple Skolemization Springer Science+Business Media structure subqueries subsets syntax Theorem tuples values