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Appropriate inferences of data dependencies in relational databases

  • Joachim Biskup
  • Sebastian Link
Article

Abstract

We study inference systems for the combined class of functional and full hierarchical dependencies in relational databases. Two notions of implication are considered: the original notion in which a dependency is implied by a given set of dependencies and the underlying set of attributes, and the alternative notion in which a dependency is implied by a given set of dependencies alone. The first main result establishes a finite axiomatisation for the original notion of implication which clarifies the role of the complementation rule in the combined setting. In fact, we identify inference systems that are appropriate in the following sense: full hierarchical dependencies can be inferred without use of the complementation rule at all or with a single application of the complementation rule at the final step of the inference only; and functional dependencies can be inferred without any application of the complementation rule. The second main result establishes a finite axiomatisation for the alternative notion of implication. We further show how inferences of full hierarchical dependencies can be simulated by inferences of multivalued dependencies, and vice versa. This enables us to apply both of our main results to the combined class of functional and multivalued dependencies. Furthermore, we establish a novel axiomatisation for the class of non-trivial functional dependencies.

Keywords

Axiomatisation Data semantics Full hierarchical dependency Functional dependency Implication Inference Multivalued dependency Relational database 

Mathematics Subject Classifications (2010)

03B70 68P15 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Fakultät für InformatikTechnische Universität DortmundDortmundGermany
  2. 2.Department of Computer ScienceThe University of AucklandAucklandNew Zealand

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