This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator @math for aggregate programs, independently proposed This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates. To appear in Theory and Practice of Logic Programming (TPLP).
This notion of unfolding derives from the work on unfolding of intensional sets @cite_8 , and has been independently described in @cite_5 .
@cite_5 @cite_8
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Dept. of Computer Science, K.U.LeuvenCelestijnenlaan 200A, B-3001 Heverlee, BelgiumE-mail: pelov,marcd,maurice @cs.kuleuven.ac.beAbstract. We deﬁne a translation of aggregate programs to normal lo-gic programs which preserves the set of partial stable models. We thendeﬁne the classes of deﬁnite and stratiﬁed aggregate programs and showthat the translation of such programs are, respectively, deﬁnite and strat-iﬁed logic programs. Consequently these two classes of programs havea single partial stable model which is two-valued and is also the well-founded model. Our deﬁnition of stratiﬁcation is more general than theexisting one and covers a strictly larger class of programs. The aim of this paper is to extend theConstructive Negation technique to the case ofCLP(SeT), a Constraint Logic Programming (CLP) language based on hereditarily (and hybrid) finite sets. The challenging aspects of the problem originate from the fact that the structure on whichCLP(SeT) is based is notadmissible closed, and this does not allow to reuse the results presented in the literature concerning the relationships betweenCLP and constructive negation.