Study of Implication Representation Based on Decision Implication

Abstract

Formal concept analysis can use concept lattice and (attribute) implication to visualize and represent knowledge. Decision implication is a special implication, and the study of decision implication is to establish and study one or more closed subsystems in implications, including decision implication subsystem and corresponding semantic and syntactic subsystems. In order to further clarify the relationship between implications and decision implications, it is studied whether the implication systems can be obtained from these decision implications subsystems. In fact, if implications can be deduced from decision implications, the studies on implications and canonical basis can be reduced to the studies of decision implications and decision implication canonical basis. Firstly, some sufficient and necessary conditions are given to determine whether implications can be represented by decision implication. Secondly, an example is given to show that there are some implications that cannot be represented by decision implications, and thus the representation of implications is further divided into direct and indirect representations. Finally, by studying the characteristics of the implication that cannot be directly represented when there is only one decision attribute in decision contexts, a sufficient and necessary condition is presented to determine whether implications cannot be directly represented by decision implication, and a generation method is also designed to generate the implications that cannot be directly represented. This study provides a new perspective for the study of implications and canonical basis, and also forms a foundation for further theoretical study on formal concept analysis.

Keywords

• formal concept analysis (fca)
• concept lattice
• implication
• decision implication