Foundations of Aggregation in Deductive Databases

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.