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Lattices with Interior and Closure Operators and Abstract Approximation Spaces

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Transactions on Rough Sets X

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5656))

Abstract

The non–equational notion of abstract approximation space for roughness theory is introduced, and its relationship with the equational definition of lattice with Tarski interior and closure operations is studied. Their categorical isomorphism is proved, and the role of the Tarski interior and closure with an algebraic semantic of a S4–like model of modal logic is widely investigated.

A hierarchy of three particular models of this approach to roughness based on a concrete universe is described, listed from the stronger model to the weaker one: (1) the partition spaces, (2) the topological spaces by open basis, and (3) the covering spaces.

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Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università di Milano – Bicocca, Viale Sarca 336–U14, I–20126, Milano, Italia

    Gianpiero Cattaneo & Davide Ciucci

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  1. Gianpiero Cattaneo
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  2. Davide Ciucci
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Winnipeg, University of Manitoba, R3T 5V6, Manitoba, Canada

    James F. Peters

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

    Andrzej Skowron

  3. Department of Logic and Philosophy of Science, Maria Curie-Skłodowska University, Marii Curie-Skłodowskiej 4, 20-031, Lublin, Poland

    Marcin Wolski

  4. University of Calcutta, Kolkata, India

    Mihir K. Chakraborty

  5. Zhejiang Ocean University, Zhejiang, P.R. China

    Wei-Zhi Wu

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Cattaneo, G., Ciucci, D. (2009). Lattices with Interior and Closure Operators and Abstract Approximation Spaces. In: Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, WZ. (eds) Transactions on Rough Sets X. Lecture Notes in Computer Science, vol 5656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03281-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-03281-3_3

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