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The Double-Level Default Description Logic \(\mathcal {D}3\mathcal {L}\)

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Knowledge Science, Engineering and Management (KSEM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9403))

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Abstract

We propose the default description logic \(\mathcal {D}2\mathcal {L}\) and the double-level default description logic \(\mathcal {D}3\mathcal {L}\). \(\mathcal {D}2\mathcal {L}\) embeds normal defaults inside the basic description logic \(\mathcal {ALC},\) and \(\mathcal {D}3\mathcal {L}\) augments \(\mathcal {D}2\mathcal {L}\) with normal double-level defaults. Double-level defaults are defaults of defaults and can be used to represent default inheritance of default properties of concepts in ontologies. A \(\mathcal {D}3\mathcal {L}\) knowledge base (\(\mathcal {D}3\mathcal {L}\)-KB) can be divided into two levels of knowledge bases, and correspondingly its extensions can be computed in two steps. \(\mathcal {D}3\mathcal {L}\) is more expressive than \(\mathcal {D}2\mathcal {L}\) since there is a \(\mathcal {D}3\mathcal {L}\)-KB that cannot reduce to any \(\mathcal {D}2\mathcal {L}\)-KB. Specifically, there is a \(\mathcal {D}3\mathcal {L}\)-KB such that the set of all its extensions cannot be exactly generated by any \(\mathcal {D}2\mathcal {L}\)-KB.

The work is supported by NSFC grants (No. 91224006, No. 61173063, and No. 61203284) and a MOST grant (No. 201303107).

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, No. 4, South 4th Street, Zhongguancun, Haidian District, Beijing, 100190, China

    Liangjun Zang

  2. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, No. 6 Kexueyuan South Road, Haidian District, Beijing, 100190, China

    Bo Chen & Cungen Cao

  3. School of Computer Science and Engineering, Jiangsu University of Science and Technology, No. 2 Mengxi Road, Zhenjiang, 212003, Jiangsu, China

    Weimin Wang

Authors
  1. Liangjun Zang
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  2. Weimin Wang
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  3. Bo Chen
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  4. Cungen Cao
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Corresponding author

Correspondence to Liangjun Zang .

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Editors and Affiliations

  1. Chinese Academy of Sciences, Beijing, China

    Songmao Zhang

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Martin Wirsing

  3. Southwest University, Chongqing, China

    Zili Zhang

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© 2015 Springer International Publishing Switzerland

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Zang, L., Wang, W., Chen, B., Cao, C. (2015). The Double-Level Default Description Logic \(\mathcal {D}3\mathcal {L}\). In: Zhang, S., Wirsing, M., Zhang, Z. (eds) Knowledge Science, Engineering and Management. KSEM 2015. Lecture Notes in Computer Science(), vol 9403. Springer, Cham. https://doi.org/10.1007/978-3-319-25159-2_12

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  • DOI: https://doi.org/10.1007/978-3-319-25159-2_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25158-5

  • Online ISBN: 978-3-319-25159-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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