An algebraic formulation of the aggregative closure query

The aggregative closure problem, a transitive closure problem with aggregations on transitive paths, is formally defined by database terms. Its definition in our paper holds only on the subset conditions of path algebra, thereby it is more general than other definitions in previous works. For the completion of the definition, we suggest conditions for the existence of the fixpoint and classified the conditions as the properties of the aggregate operators and the problem domain. So we can verify the existence of the fixpoint by the suggested conditions. The naive algorithm is proposed as a computational semantics for the aggregative closure problem. This study also proves that for an aggregative closure problem the semi-naive algorithm is computationally equivalent to the naive algorithm when the aggregate product operator is distributive over aggregate sum operator.