Axiomatic characterizations of dual concept lattices

  • Authors:

  • Jian-Min Ma;Wen-Xiu Zhang

  • Affiliations:

  • Department of Mathematics and Information Science, Faculty of Science, Chang'an University, Xi'an, Shaan'xi 710064, PR China;Institute for Information and System Sciences, Faculty of Science, Xi'an Jiaotong University, Xi'an, Shaan'xi 710049, PR China

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2013

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Abstract

Formal concept analysis is an algebraic model based on a Galois connection. It is used for symbolic knowledge exploration from an elementary form of a formal context. This paper mainly presents a general framework for concept lattice in which axiomatic approaches are used. The relationship between concept lattice and dual concept lattice is first studied. Based on set-theoretic operators, generalized concept systems are established. And properties of them are examined. By using axiomatic approaches, a pair of dual concept lattices is characterized by different sets of axioms. The connections between 0-1 binary relations and generalized concept systems are examined. And generalized dual concept systems can be constructed by a pair of dual set-theoretic operators. Axiomatic characterizations of the generalized concept systems guarantee the existence of a binary relation producing a formal context.