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Independence of axiom sets characterizing formal concepts

  • Xiao-Xue Song
  • Xia Wang
  • Wen-Xiu Zhang
Original Article

Abstract

The theory of concept lattice proposed by Wille has been generalized in three different ways based on binary formal contexts, and substantive properties with respect to these formal concepts have been derived. In this paper, we study a reverse problem, that is, how to characterize the notions of formal concepts in terms of their properties. Axiomatic characterizations for the theory of formal concept analysis are presented. By this approach, four types of conceptual knowledge system are defined, and axiom sets that must be satisfied by the conceptual knowledge system are stated. It is proved that axioms of the conceptual knowledge system guarantee the existence of certain types of binary relations producing the same formal concepts. The independence of axiom sets characterizing the conceptual knowledge system is examined.

Keywords

Concept lattices Axioms Independence Conceptual knowledge systems 

Notes

Acknowledgments

This work was supported by grants from the National Natural Science Foundation of China (No. 61005042) and Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 09JK811).

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyXianyang Normal UniversityXianyangPeople’s Republic of China
  2. 2.School of Mathematics, Physics and Information SciencesZhejiang Ocean UniversityZhoushanPeople’s Republic of China
  3. 3.Faculty of Science, Institute for Information and System Sciences Xi’an Jiaotong UniversityXi’anPeople’s Republic of China

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