Towards Well-behaved Semantics Suitable for Aggregation

Real Applications of Databases ask for the notion of Aggrega-tion. This, however, needs stronger semantics as usual. In particular, such semantics should extend the wellfounded semantics WFS. We study such extensions and determine which semantics are possible given certain abstract properties like partial evaluation, cumulativity, partial monotony and supraclassicality. While WFS + (introduced independently by Dix and Schlipf for other purposes) has recently been shown by Osorio and Jayaraman to be well suited for aggregation, it has higher complexity than WFS: it is on the rst level of the polynomial hierarchy. We present in this paper polynomial-time computable semantics which are also well suited. Our deenitions use a connuent and terminating calculus introduced by Brass and Dix and further reened by Brass, Freitag and Zukowski. This allows us to generalize our results to disjunctive logic programs. Finally, such semantics can also be used to improve the stable semantics by extending its scope (the class of programs where STABLE is consistent).