Formal concept analysis and rough set theory from the perspective of finite topological approximations

  • Authors:
  • Marcin Wolski

  • Affiliations:
  • Department of Logic and Methodology of Science, Maria Curie-Skłodowska University, Poland

  • Venue:
  • Transactions on Rough Sets III
  • Year:
  • 2005

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Abstract

The paper examines Formal Concept Analysis (FCA) and Rough Set Theory (RST) against the background of the theory of finite approximations of continuous topological spaces. We define the operators of FCA and RST by means of the specialisation order on elements of a topological space X which induces a finite approximation of X. On this basis we prove that FCA and RST together provide a semantics for tense logic S4.t. Moreover, the paper demonstrates that a topological space X cannot be distinguished from its finite approximation by means of the basic temporal language. It means that from the perspective of topology S4.t is a better account of approximate reasoning then unimodal logics, which have been typically employed.