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A Cartesian Closed Category of Approximable Concept Structures

  • Pascal Hitzler
  • Guo-Qiang Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3127)

Abstract

Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the two areas as outlined in [25]. Building on a new notion of approximable concept introduced by Zhang and Shen [26], this paper provides an appropriate notion of morphisms on formal contexts and shows that the resulting category is equivalent to (a) the category of complete algebraic lattices and Scott continuous functions, and (b) a category of information systems and approximable mappings. Since the latter categories are cartesian closed, we obtain a cartesian closed category of formal contexts that respects both the context structures as well as the intrinsic notion of approximable concepts at the same time.

Keywords

Category Theory Complete Lattice Concept Lattice Approximable Mapping Domain Theory 
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 2004

Authors and Affiliations

  • Pascal Hitzler
    • 1
  • Guo-Qiang Zhang
    • 2
  1. 1.Artificial Intelligence Institute, Department of Computer ScienceDresden University of TechnologyDresdenGermany
  2. 2.Department of Electrical Engineering and Computer ScienceCase Western Reserve UniversityClevelandU.S.A.

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