{"type":"ScholarlyArticle","title":"Declarative and Computational Properties of Logic Programs with Aggregates","authors":[{"name":"Francesco Calimeri","slug":"francesco-calimeri","given":"Francesco","family":"Calimeri","affiliation":""},{"name":"Wolfgang Faber","slug":"wolfgang-faber","given":"Wolfgang","family":"Faber","affiliation":""},{"name":"Nicola Leone","slug":"nicola-leone","given":"Nicola","family":"Leone","affiliation":""},{"name":"Simona Perri","slug":"simona-perri","given":"Simona","family":"Perri","affiliation":""}],"abstract":"We investigate the properties of logic programs with aggregates. We mainly focus on programs with monotone and antimonotone aggregates (LPA m,a programs). We define a new notion of unfounded set for LPA 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 LPA m,a program are precisely its unfounded-free models. We define a well-founded operator WP for LPA m,a programs; we prove that its total fixpoints are precisely 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 efficiently computable, and for aggregate-free programs it coincides with the well-founded model. We carry out an in-depth complexity analysis in the general framework, including also nonmonotone aggregates. We prove that monotone and antimonotone aggregates do not increase the complexity of cautious reasoning, which remains in co-NP. Nonmonotone aggregates, instead, do increase the complexity by one level in the polynomial hierarchy. Our results allow also to generalize and speedup ASP systems with aggregates.","doi":null,"url":"https://ijcai.org/proceedings/2005/166","pdf":"https://ijcai.org/proceedings/2005/0166.pdf","markdown":"https://ijcai.org/proceedings/2005/166.md","bibtex":"https://ijcai.org/proceedings/2005/bibtex/166","volume":{"slug":"2005","title":"Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2005","url":"https://ijcai.org/proceedings/2005/","year":2005,"location":"Edinburgh, Scotland, UK","dates":"","editors":"","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":166,"pages":{"first":406,"last":410},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}