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T. Dell´Armi, W. Faber, G. Ielpa, N. Leone, G. Pfeifer:
"Aggregate Functions in Disjunctive Logic Programming: Semantics,Complexity,and Implementation in DLV";
in: "Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI) 2003", Elsevier Science Publishers, 2003, ISBN: 0-127-05661-0, S. 847 - 852.

Disjunctive Logic Programming (DLP) is a very expressive formalism:
it allows to express every property of finite structures that is
decidable in the complexity class Σ^P₂ (NP^NP).
Despite the high expressiveness of DLP, there are some simple properties, often arising in
real-world applications,
which cannot be encoded in a simple and natural manner.
Among these, properties requiring to apply some arithmetic operators
(like sum, times, count) on a set of elements satisfying some conditions,
cannot be naturally expressed in DLP.
To overcome this deficiency,
in this paper we extend DLP by aggregate functions.
We formally define the semantics of the new language, named
DLP^A.
We show the usefulness of the new constructs on relevant
knowledge-based problems.
We analyze the computational complexity of DLP^A, showing
that the addition of aggregates does not bring a higher cost in that respect.
We provide an implementation of the DLP^A in DLV -- the state-of-the-art DLP system -- and
report on experiments which confirm the usefulness of the proposed extension also
for the efficiency of the computation.

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