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Alternating Fixpoint Operator for Hybrid MKNF Knowledge Bases as an Approximator of AFT

Published online by Cambridge University Press:  01 September 2021

FANGFANG LIU Open the ORCID record for FANGFANG LIU [Opens in a new window]  and
JIA-HUAI YOU Open the ORCID record for JIA-HUAI YOU [Opens in a new window]
FANGFANG LIU
Affiliation:
School of Computer Engineering and Science, Shanghai University, Shanghai, China (e-mail: [email protected])
JIA-HUAI YOU
Affiliation:
Department of Computing Science, University of Alberta, Edmonton, Canada (e-mail: [email protected])
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Abstract

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Approximation fixpoint theory (AFT) provides an algebraic framework for the study of fixpoints of operators on bilattices and has found its applications in characterizing semantics for various classes of logic programs and nonmonotonic languages. In this paper, we show one more application of this kind: the alternating fixpoint operator by Knorr et al. for the study of the well-founded semantics for hybrid minimal knowledge and negation as failure (MKNF) knowledge bases is in fact an approximator of AFT in disguise, which, thanks to the abstraction power of AFT, characterizes not only the well-founded semantics but also two-valued as well as three-valued semantics for hybrid MKNF knowledge bases. Furthermore, we show an improved approximator for these knowledge bases, of which the least stable fixpoint is information richer than the one formulated from Knorr et al.’s construction. This leads to an improved computation for the well-founded semantics. This work is built on an extension of AFT that supports consistent as well as inconsistent pairs in the induced product bilattice, to deal with inconsistencies that arise in the context of hybrid MKNF knowledge bases. This part of the work can be considered generalizing the original AFT from symmetric approximators to arbitrary approximators.

Keywords

approximation fixpoint theoryhybrid MKNF knowledge baseslogic programsanswer set semanticsdescription logicsinconsistencies
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 22 , Issue 2: Special Issue on the International Joint Conference on Rules and Reasoning, RuleML+RR 2019 , March 2022 , pp. 305 - 334
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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