Aggregation in Disjunctive Deductive Databases

Practical applications of deductive databases often require the use of extended features like disjunctive information, aggregation operators or default negation. But it has been unclear how one could deal with aggregation in the presense of recursion and disjunction. Usually , there is the requirement that deductive databases must be stratiied w.r.t. aggregation, i.e. a predicate q that is deened using aggrega-tion based on some other predicate p may not be used for deriving this other predicate p. Disjunctive deductive databases extend the classical Datalog language by disjunction, default negation, and function symbols. 1 There are practical examples that require non{ stratiied aggregation in disjunctive deductive databases. We will present a clear declarative set semantics for disjunctive deductive databases P with aggregation. The semantics is based on a special program transformation, which replaces an aggregation by a suitable construct using default negation and the function symbol for lists. The transformed database P agg is free of aggre-gation, and it can be evaluated based on the well{known concept of stable models. 1 In this paper we will use the term disjunctive de-ductive database as an equivalent to disjunctive logic program.