MONOTONIC AGGREGATION IN DEDUCTIVE DATABASES

We propose a semantics for aggregates in deductive databases based on a notion of minimality. Unlike some previous approaches, we form a min imal model of a program component including aggregate operators, rathe r than insisting that the aggregate apply to atoms that have been full y determined or that aggregate functions are rewritten in terms of neg ation. In order to guarantee the existence of such a minimal model we need to insist that the domains over which we are aggregating are comp lete lattices and that the program is in a sense monotonic. Our approa ch generalizes previous approaches based on the well-founded semantics and various forms of stratification. We are also able to handle a lar ge variety of monotonic (or pseudo-monotonic) aggregate functions. (C) 1997 Academic Press.