{"type":"ScholarlyArticle","title":"Partial Grounded Fixpoints","authors":[{"name":"Bart Bogaerts","slug":"bart-bogaerts","given":"Bart","family":"Bogaerts","affiliation":""},{"name":"Joost Vennekens","slug":"joost-vennekens","given":"Joost","family":"Vennekens","affiliation":""},{"name":"Marc Denecker","slug":"marc-denecker","given":"Marc","family":"Denecker","affiliation":""}],"abstract":"Approximation fixpoint theory (AFT) is an algebraical study of fixpoints of lattice operators. Recently, AFT was extended with the notion of a grounded fixpoint. This type of fixpoint formalises common intuitions from various application domains of AFT, including logic programming, default logic, autoepistemic logic and abstract argumentation frameworks. The study of groundedness was limited to exact lattice points; in this paper, we extend it to the bilattice: for an approximator A of O, we define A-groundedness. We show that all partial A-stable fixpoints are A-grounded and that the A-well-founded fixpoint is uniquely characterised as the least precise A-grounded fixpoint. We apply our theory to logic programming and study complexity.","doi":null,"url":"https://ijcai.org/proceedings/2015/394","pdf":"https://ijcai.org/proceedings/2015/0394.pdf","markdown":"https://ijcai.org/proceedings/2015/394.md","bibtex":"https://ijcai.org/proceedings/2015/bibtex/394","volume":{"slug":"2015","title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2015","url":"https://ijcai.org/proceedings/2015/","year":2015,"location":"Buenos Aires, Argentina","dates":"25–31 July 2015","editors":"Qiang Yang and Michael Wooldridge","isbn":"978-1-57735-738-4","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Special Track on Knowledge Representation and Reasoning","track":"Special Track on Knowledge Representation and Reasoning","number":394,"pages":{"first":2784,"last":2789},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}