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Theoretical aspects of data management include, among other areas, the foundations of query languages, computational complexity and expressive power of queries, finite model theory, database design theory, dependency theory, foundations of concurrency control and database recovery, deductive databases, temporal and spatial databases, real time databases, managing uncertain data and probabilistic databases, and Web data.
Most research work has traditionally been based on the relational model, since this model is usually considered the simplest and most foundational model of interest. Corresponding results for other data models, such as object-oriented or semi-structured models, or, more recently, graph data models and XML, are often derivable from those for the relational model.
A central focus of database theory is on understanding the complexity and power of query languages and their connection to logic. Starting from relational algebra and first-order logic (which are equivalent by Codd's theorem) and the insight that important queries such as graph reachability are not expressible in this language, more powerful language based on logic programming and fixpoint logic such as datalog were studied. Another focus was on the foundations of query optimization and data integration. Here most work studied conjunctive queries, which admit query optimization even under constraints using the chase algorithm.
- Abiteboul, Serge; Hull, Richard B.; Vianu, Victor (1995), Foundations of Databases, Addison-Wesley, ISBN 0-201-53771-0
- David Maier, The Theory of Relational Databases. Copyright 1983 David Maier. Available at http://web.cecs.pdx.edu/~maier/TheoryBook/TRD.html