Abstract
As a foundation for providing semantics for aggregation within recursion, the structure of subsets of partially ordered domains is studied. We argue that the underlying cause of many of the difficulties encountered in extending deductive database semantics to include aggregation is that set construction does not preserve the structure of the underlying domain very well. We study a binary relation ⊏ that is stronger than the standard ⊂, contrasting its properties on domains with differing amounts of structure. An analogous ≻ is defined that is more appropriate than R[ for minimization problems.
A class of aggregate functions, based on structural recursion, is defined formally. Proposed language constructs permit users to define their own interpreted functions and aggregates.
Several relational algebra operations are not monotonic w.r.t. ⊏. To overcome this problem, unfolding is proposed to “bury” the nonmonotonic operations inside aggregation.
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© 1993 Springer-Verlag Berlin Heidelberg
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Van Gelder, A. (1993). Foundations of aggregation in deductive databases. In: Ceri, S., Tanaka, K., Tsur, S. (eds) Deductive and Object-Oriented Databases. DOOD 1993. Lecture Notes in Computer Science, vol 760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57530-8_2
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DOI: https://doi.org/10.1007/3-540-57530-8_2
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