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 di culties 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 di ering amounts of structure. An analogous is de ned that is more appropriate than < for minimization problems. A class of aggregate functions, based on structural recursion, is de ned formally. Proposed language constructs permit users to de ne 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.