Abstract
We study an approach to relational databases which treats relations not as subsets of a Cartesian product but as subsets of some domain — a partially ordered space of descriptions. This approach permits generalizations of relations that admit null values and variants. In previous work it was shown how to define the notion of a relation scheme in such a setting. Here we provide a characterization of a scheme that is more general, and show that operations analogous to projection, selection and join retain the desired properties. Schemes also allow us to develop dependency theory for such generalized relations. An extension of this model is described which admits a set constructor and is therefore useful for the study of higher-order relations and their generalizations.
Supported in part by NSF Grants IRI-86-10617 and CCR-90-57570 and ONR Grant NOOO14-88-K0634
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Libkin, L. (1991). A relational algebra for complex objects based on partial information. In: Thalheim, B., Demetrovics, J., Gerhardt, H.D. (eds) MFDBS 91. MFDBS 1991. Lecture Notes in Computer Science, vol 495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54009-1_3
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DOI: https://doi.org/10.1007/3-540-54009-1_3
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