Axiomatic characterizations of dual concept lattices

作者：Ma, Jian-Min^*; Zhang, Wen-Xiu

来源：International Journal of Approximate Reasoning, 2013, 54(5): 690-697.

DOI：10.1016/j.ijar.2013.01.007

• Formal context
• Concept lattice
• Generalized concept system
• Set-theoretic operator
• Dual operator

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.

• 出版日期2013-7
• 单位长安大学; 西安交通大学