Definition
The study of expressive power concentrates on comparing classes of queries that can be expressed in different languages, and on proving expressibility - or inexpressibility - of certain queries in a query language.
Historical Background
Ever since Codd proposed relational calculus (first-order predicate logic) as a basic relational query language, it has been common for database query languages to have limited expressiveness. If a language cannot express everything computable, then it is natural to ask:
- 1.
What queries cannot be expressed in a language ℒ
- 2.
Which methods are available for proving such results?
Furthermore, if there are two query languages ℒ1 and ℒ2, one may want to compare their expressiveness: for example, ℒ1 ⊈ ℒ2 means that all queries expressible in ℒ1 are also expressible in ℒ2, but there are queries expressible in ℒ2 that are not expressible in ℒ1.
In 1975, Fagin [4] showed that queries such as the transitive closure of a graph and connectivity test...
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Libkin, L. (2018). Expressive Power of Query Languages. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_1239
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