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

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

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摘要

Approximation fixpoint theory (AFT) provides an algebraic framework for the study of fixpointsof operators on bilattices and has found its applications in characterizing semantics forvarious classes of logic programs and nonmonotonic languages. In this paper, we show one moreapplication of this kind: the alternating fixpoint operator by Knorr et al. for the study of thewell-founded semantics for hybrid minimal knowledge and negation as failure (MKNF) knowledgebases is in fact an approximator of AFT in disguise, which, thanks to the abstractionpower of AFT, characterizes not only the well-founded semantics but also two-valued as well asthree-valued semantics for hybrid MKNF knowledge bases. Furthermore, we show an improvedapproximator for these knowledge bases, of which the least stable fixpoint is information richerthan the one formulated from Knorr et al.’s construction. This leads to an improved computationfor the well-founded semantics. This work is built on an extension of AFT that supportsconsistent as well as inconsistent pairs in the induced product bilattice, to deal with inconsistenciesthat arise in the context of hybrid MKNF knowledge bases. This part of the workcan be considered generalizing the original AFT from symmetric approximators to arbitraryapproximators.

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