Declarative and Computational Properties of Logic Programs with Aggregates.
Francesco Calimeri, Wolfgang Faber, Nicola Leone, Simona Perri · 2005
We investigate the properties of logic programs with aggregates. We mainly focus on programs with monotone and antimonotone aggregates (LP A m,a programs). We define a new notion of unfounded set for LP A m,a programs, and prove that it is a sound generalization of the standard notion of unfounded set for aggregate-free programs. We show that the answer sets of an LP A m,a program are precisely its unfounded-free models. We define a well-founded operator WP for LP A m,a programs; we prove that its total fixpoints are pre-cisely the answer sets of P, and its least fixpoint Wω P (∅) is contained in the intersection of all answer sets (if P admits an answer set). Wω P (∅) is