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Logic for Rough Sets with Rough Double Stone Algebraic Semantics

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Part of the book series:Lecture Notes in Computer Science ((LNAI,volume 3641))

Abstract

Many researchers study rough sets from the point of view of description of the rough set pairs(a rough set pair is also called a rough set), i.e. <lower approximation set, upper approximation set>. An important result is that the collection of rough sets of an approximation space can be made into a regular double Stone algebra. In this paper, a logic for rough sets, i.e., the sequent calculus corresponding to rough double Stone algebra, is proposed. The syntax and semantics are defined. The soundless and completeness are proved.

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Author information

Authors and Affiliations

  1. Institute of Artificial Intelligence, Zhejiang University, Hangzhou, 310012, P.R. China

    Jian-Hua Dai

Authors
  1. Jian-Hua Dai

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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, SK, S4S 0A2 Canada, Polish-Japanese Institute of Information Technology, Koszykowa 86, 02-008 Warsaw, P.O. Box, Poland

    Dominik Ślęzak

  2. School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, P.R. China

    Guoyin Wang

  3. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Marcin Szczuka

  4. Department of Computer Science, Brock University, St. Catharines, L2S 3A1, Ontario, Canada

    Ivo Düntsch

  5. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

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© 2005 Springer-Verlag Berlin Heidelberg

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Dai, JH. (2005). Logic for Rough Sets with Rough Double Stone Algebraic Semantics. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_15

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