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Knowledge and Systems Engineering pp 135–145Cite as

Heyting-Brouwer Rough Set Logic

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 245))

Abstract

A rough set logic based on Heyting-Brouwer algebras HBRSL is proposed as a basis for reasoning about rough information. It is an extension of Düntsch’s logic with intuitionistic implication, and is seen as a variant of Heyting- Brouwer logic. A Kripke semantics and natural deduction for the logic are presented and the completeness theorem is proved.

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References

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Author information

Authors and Affiliations

  1. C-Republic, 1-20-1, Higashi-Yurigaoka, Asao-ku, Kawasaki, 215-0012, Japan

    Seiki Akama

  2. Hokkaido University, Kita 13, Nishi 8, Kita-ku, Sapporo, 080-8628, Japan

    Tetsuya Murai

  3. Muroran Institute of Technology, 27-1, Muroran, Muroran, 050-8585, Japan

    Yasuo Kudo

Authors
  1. Seiki Akama
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  2. Tetsuya Murai
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  3. Yasuo Kudo
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Corresponding author

Correspondence to Seiki Akama .

Editor information

Editors and Affiliations

  1. School of Knowledge Science, Japan Advanced Institute of Science and Technology, Ishikawa, Japan

    Van Nam Huynh

  2. UMR CNRS 7253 Heudiasyc, University of Technology of Compiegne, Compiegne Cedex, France

    Thierry Denoeux

  3. Faculty of Information Technology, Hanoi National University of Education, Hanoi, Vietnam

    Dang Hung Tran

  4. Faculty of Information Technology, University of Engineering and Technology, Hanoi, Vietnam

    Anh Cuong Le

  5. Faculty of Information Technology, University of Engineering and Technology, Hanoi, Vietnam

    Son Bao Pham

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© 2014 Springer International Publishing Switzerland

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Cite this paper

Akama, S., Murai, T., Kudo, Y. (2014). Heyting-Brouwer Rough Set Logic. In: Huynh, V., Denoeux, T., Tran, D., Le, A., Pham, S. (eds) Knowledge and Systems Engineering. Advances in Intelligent Systems and Computing, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-02821-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-02821-7_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02820-0

  • Online ISBN: 978-3-319-02821-7

  • eBook Packages: EngineeringEngineering (R0)

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