ML Anthology

Declarative and Computational Properties of Logic Programs with Aggregates

Francesco Calimeri, Wolfgang Faber, Nicola Leone, Simona Perri
IJCAI 2005 pp. 406-411
doi:10.13140/2.1.3855.4561 /ijcai/2005/calimeri2005ijcai-declarative/

Abstract

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

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Text

Calimeri et al. "Declarative and Computational Properties of Logic Programs with Aggregates." International Joint Conference on Artificial Intelligence, 2005. doi:10.13140/2.1.3855.4561

Markdown

[Calimeri et al. "Declarative and Computational Properties of Logic Programs with Aggregates." International Joint Conference on Artificial Intelligence, 2005.](https://mlanthology.org/ijcai/2005/calimeri2005ijcai-declarative/) doi:10.13140/2.1.3855.4561

BibTeX

@inproceedings{calimeri2005ijcai-declarative,
  title     = {{Declarative and Computational Properties of Logic Programs with Aggregates}},
  author    = {Calimeri, Francesco and Faber, Wolfgang and Leone, Nicola and Perri, Simona},
  booktitle = {International Joint Conference on Artificial Intelligence},
  year      = {2005},
  pages     = {406-411},
  doi       = {10.13140/2.1.3855.4561},
  url       = {https://mlanthology.org/ijcai/2005/calimeri2005ijcai-declarative/}
}