---
title: "Partial Grounded Fixpoints"
authors:
  - "Bart Bogaerts"
  - "Joost Vennekens"
  - "Marc Denecker"
doi: ""
url: "https://ijcai.org/proceedings/2015/394"
pdf: "https://ijcai.org/proceedings/2015/0394.pdf"
venue: "Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence"
year: 2015
pages: "2784-2789"
track: "Special Track on Knowledge Representation and Reasoning"
keywords:
---

# Partial Grounded Fixpoints

Bart Bogaerts, Joost Vennekens, Marc Denecker

*Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence*, pages 2784-2789.

## 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.