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On Generalization and Subsumption for Ordered Clauses

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New Frontiers in Artificial Intelligence (JSAI 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4012))

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Abstract

In this paper, we investigate the properties of ordered clauses defined as a sequence of literals. First, we show that while there exists no least generalization of two ordered clauses, every minimal generalization of them has a complete selection to which the result applying Plotkin’s algorithm is subsume-equivalent. Furthermore, we show that the number of complete selections can grow exponentially. Next, we show that the subsumption problem for ordered clauses is also NP-complete as similar as general clauses.

This work is partially supported by Grand-in-Aid for Scientific Research 15700137 and 16016275 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.

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Author information

Authors and Affiliations

  1. Graduate School of Computer Science and Systems Engineering, Japan

    Megumi Kuwabara & Takeshi Ogawa

  2. Department of Artificial Intelligence, Kyushu Institute of Technology, Kawazu 680-4, Iizuka, 820-8502, Japan

    Kouichi Hirata & Masateru Harao

Authors
  1. Megumi Kuwabara
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  2. Takeshi Ogawa
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  3. Kouichi Hirata
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  4. Masateru Harao
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Editor information

Editors and Affiliations

  1. ISIR, Osaka University, 8-1, Mihogaoka, 567-0047, Osaka, Ibaraki, Japan

    Takashi Washio

  2. CREST, Japan Science and Technology Agency, Japan

    Akito Sakurai

  3. Dept. of Information Media, Tokyo Denki University, room 1009, 10th floor, building 11, 2-2, Kandanishikicho, Chiyodaku, 101-8457, Tokyo, Japan

    Katsuto Nakajima

  4. National Institute of Informatics, 2-1-2 Chiyoda-ku, 101-8430, Tokyo, Japan

    Hideaki Takeda

  5. Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Satoshi Tojo

  6. Department of ISEE, Kyushu University, 819-0395, Fukuoka, Japan

    Makoto Yokoo

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© 2006 Springer-Verlag Berlin Heidelberg

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Kuwabara, M., Ogawa, T., Hirata, K., Harao, M. (2006). On Generalization and Subsumption for Ordered Clauses. In: Washio, T., Sakurai, A., Nakajima, K., Takeda, H., Tojo, S., Yokoo, M. (eds) New Frontiers in Artificial Intelligence. JSAI 2005. Lecture Notes in Computer Science(), vol 4012. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780496_24

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  • DOI: https://doi.org/10.1007/11780496_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35470-3

  • Online ISBN: 978-3-540-35471-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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