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Roughness by Residuals

Algebraic Description of Rough Sets and an Algorithm for Finding Core Relations

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Relational and Algebraic Methods in Computer Science (RAMICS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9348))

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Abstract

Rough set theory (RST) focuses on forming posets of equivalence relations to describe sets with increasing accuracy. The connection between modal logics and RST is well known and has been extensively studied in their relation algebraic (RA) formalisation. RST has also been interpreted as a variant of intuitionistic or multi-valued logics and has even been studied in the context of logic programming.

This paper presents a detailed formalisation of RST in RA by way of residuals, motivates its generalisation and shows how results can be used to prove many RST properties in a simple algebraic manner (as opposed to many tedious and error-prone set-theoretic proofs). A further abstraction to an entirely point-free representation shows the correspondence to Kleene algebras with domain.

Finally, we show how an RA-perspective on RST allows to derive an abstract algorithm for finding reducts from a mere analysis of the properties of the RA-construction rather than by a data-driven approach.

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Authors and Affiliations

  1. Department of Computer Science, University of Augsburg, Augsburg, Germany

    Martin E. Müller

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  1. Martin E. Müller
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Correspondence to Martin E. Müller .

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Editors and Affiliations

  1. McMaster University, Hamilton, Ontario, Canada

    Wolfram Kahl

  2. Brock University, St. Catharines, Ontario, Canada

    Michael Winter

  3. Universidade do Minho, Braga, Portugal

    José Oliveira

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Müller, M.E. (2015). Roughness by Residuals. In: Kahl, W., Winter, M., Oliveira, J. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2015. Lecture Notes in Computer Science(), vol 9348. Springer, Cham. https://doi.org/10.1007/978-3-319-24704-5_23

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  • DOI: https://doi.org/10.1007/978-3-319-24704-5_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24703-8

  • Online ISBN: 978-3-319-24704-5

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