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 version in which the underlying set of attributes is fixed, and the alternative notion in which this set is left undetermined.
The first main result establishes a finite axiomatisation in fixed universes 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; and functional dependencies can be inferred without any application of the complementation rule. The second main result establishes a finite axiomatisation for functional and full hierarchical dependencies in undetermined universes.
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Biskup, J., Link, S. (2008). Appropriate Reasoning about Data Dependencies in Fixed and Undetermined Universes. In: Hartmann, S., Kern-Isberner, G. (eds) Foundations of Information and Knowledge Systems. FoIKS 2008. Lecture Notes in Computer Science, vol 4932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77684-0_7
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DOI: https://doi.org/10.1007/978-3-540-77684-0_7
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