Partial Grounded Fixpoints
Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence. Special Track on Knowledge Representation and Reasoning. 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.
@inproceedings{ijcai2015p394,
title = {Partial Grounded Fixpoints},
author = {Bogaerts, Bart and Vennekens, Joost and Denecker, Marc},
booktitle = {Proceedings of the Twenty-Fourth International Joint Conference on
Artificial Intelligence, {IJCAI-15}},
publisher = {International Joint Conferences on Artificial Intelligence},
editor = {Qiang Yang and Michael Wooldridge},
pages = {2784--2789},
year = {2015},
month = {7},
note = {Special Track on Knowledge Representation and Reasoning},
url = {https://ijcai.org/proceedings/2015/394},
}
TY - CPAPER TI - Partial Grounded Fixpoints AU - Bogaerts, Bart AU - Vennekens, Joost AU - Denecker, Marc T2 - Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-15 PB - International Joint Conferences on Artificial Intelligence PY - 2015 SP - 2784 EP - 2789 UR - https://ijcai.org/proceedings/2015/394 ER -Copied
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