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

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Rules and Reasoning (RuleML+RR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11784))

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Abstract

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 types 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. [8] for the study of well-founded semantics for hybrid MKNF knowledge bases is in fact an approximator of AFT in disguise, which, thanks to the power of abstraction 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.

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Notes

  1. 1.

    We can in addition require that an approximator A be consistent for at least one exact pair. This will eliminate the undesired situation that if a \(\le _p\)-monotone operator A is inconsistent on each exact pair, then it approximates every operator O, trivially.

  2. 2.

    In [6], A-contracting pairs were called A-reliable.

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Authors and Affiliations

  1. School of Computer Engineering and Science, Shanghai University, 99 Shangda Road, BaoShan District, Shanghai, 20444, People’s Republic of China

    Fangfang Liu

  2. Department of Computing Science, University of Alberta, Edmonton, Canada

    Jia-Huai You

Authors
  1. Fangfang Liu
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  2. Jia-Huai You
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Correspondence to Fangfang Liu .

Editor information

Editors and Affiliations

  1. Stony Brook University, Stony Brook, NY, USA

    Paul Fodor

  2. Free University of Bozen-Bolzano, Bolzano, Italy

    Marco Montali

  3. Free University of Bozen-Bolzano, Bolzano, Italy

    Diego Calvanese

  4. SINTEF AS, Oslo, Norway

    Dumitru Roman

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Liu, F., You, JH. (2019). Alternating Fixpoint Operator for Hybrid MKNF Knowledge Bases as an Approximator of AFT. In: Fodor, P., Montali, M., Calvanese, D., Roman, D. (eds) Rules and Reasoning. RuleML+RR 2019. Lecture Notes in Computer Science(), vol 11784. Springer, Cham. https://doi.org/10.1007/978-3-030-31095-0_8

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  • DOI: https://doi.org/10.1007/978-3-030-31095-0_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31094-3

  • Online ISBN: 978-3-030-31095-0

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