Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
The Ha¨rtig quantifier: a survey
Journal of Symbolic Logic
How to fit generalized quantifiers into terminological logics
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
Providing better support for a class of decision support queries
SIGMOD '96 Proceedings of the 1996 ACM SIGMOD international conference on Management of data
Safety, domain independence and generalized quantification
Data Engineering
Logics with aggregate operators
Journal of the ACM (JACM)
Applications of Logic Databases
Applications of Logic Databases
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Unary Quantifiers on Finite Models
Journal of Logic, Language and Information
Improving SQL with Generalized Quantifiers
ICDE '95 Proceedings of the Eleventh International Conference on Data Engineering
ICDT '92 Proceedings of the 4th International Conference on Database Theory
Groupwise Processing of Relational Queries
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
Theoretical Computer Science - Database theory
A family of query languages with generalized quantifiers: its definition, properties and expressiveness
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In first order logic there are two main extensions to quantification: generalized quantifiers and non-linear prefixes. While generalized quantifiers have been explored from a database perspective, non-linear prefixes have not-most likely because of complexity concerns. In this paper we first illustrate the usefulness of non-linear prefixes in query languages by means of example queries. We then introduce the subject formally, distinguishing between two forms of non-linearity: branching and cumulation. To escape complexity concerns, we focus on monadic quantifiers. In this context, we show that branching does not extend the expressive power of first order logic when it is interpreted over finite models, while cumulation does not extend the expressive power when it is interpreted over bounded models. Branching and cumulation do, however, allow us to formulate some queries in a succinct and elegant manner. When branching and cumulation are interpreted over infinite models, we show that the resulting language can be embedded in an infinitary logic proposed by Libkin. We also discuss non-linear prefixes from an algorithmic point of view.