Lattices with Interior and Closure Operators and Abstract Approximation Spaces

  • Gianpiero Cattaneo
  • Davide Ciucci
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5656)


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.


Modal Logic Boolean Algebra Closure Operator Approximation Space Kripke Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gianpiero Cattaneo
    • 1
  • Davide Ciucci
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità di Milano – BicoccaMilanoItalia

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