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International Conference on Knowledge Science, Engineering and Management

KSEM 2017: Knowledge Science, Engineering and Management pp 106–116Cite as

R-Calculus for the Primitive Statements in Description Logic \(\mathcal{ALC}\)

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10412))

Abstract

The AGM postulates [1] are for the belief revision (revision by a single belief), and the DP postulates [14] are for the iterated revision (revision by a finite sequence of beliefs). Li [4] gave an R-calculus for R-configurations \(\Delta |\Gamma \), where \(\Delta \) is a set of atomic formulas or negations of atomic formulas, and \(\Gamma \) is a finite set of formulas. With an idea to delete the requirement that \(\Delta \) is a set of atoms, we will give an R-calculus S \(^\mathrm{DL}\) (a set of deduction rules) with respect to \(\subseteq \)-minimal change such that for any finite consistent sets \(\Gamma ,\Delta \) of statements in the description logic \(\mathcal{ALC}\), there is a consistent subset \(\Theta \subseteq \Gamma \) of statements such that \(\Delta |\Gamma \Rightarrow \Delta ,\Theta \) is provable; and prove that S \(^\mathrm{DL}\) is sound and complete with the \(\subseteq \)-minimal change.

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Acknowledgments

This work was supported by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. SKLSDE-2010KF-06, Beijing University of Aeronautics and Astronautics, by the National Natural Science Foundation of China (Grant No. 91224006, 61173063, 61035004, 61203284), by the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901, and by the CNSSF 10AYY003.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Yuhui Wang, Cungen Cao & Yuefei Sui

  2. School of Computer and Control Engineering, University of Chinese Academy of Sciences, Beijing, China

    Yuhui Wang & Yuefei Sui

Authors
  1. Yuhui Wang
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  2. Cungen Cao
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  3. Yuefei Sui
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Corresponding author

Correspondence to Yuhui Wang .

Editor information

Editors and Affiliations

  1. Deakin University, Burwood, Victoria, Australia

    Gang Li

  2. University of Arizona, Tucson, Arizona, USA

    Yong Ge

  3. Southwest University, Chongqing, China

    Zili Zhang

  4. Peking University, Beijing, China

    Zhi Jin

  5. University of Technology Sydney, Sydney, New South Wales, Australia

    Michael Blumenstein

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Wang, Y., Cao, C., Sui, Y. (2017). R-Calculus for the Primitive Statements in Description Logic \(\mathcal{ALC}\) . In: Li, G., Ge, Y., Zhang, Z., Jin, Z., Blumenstein, M. (eds) Knowledge Science, Engineering and Management. KSEM 2017. Lecture Notes in Computer Science(), vol 10412. Springer, Cham. https://doi.org/10.1007/978-3-319-63558-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-63558-3_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63557-6

  • Online ISBN: 978-3-319-63558-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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