Some properties of evaluated implications used in knowledge-based systems and data-mining

The core of expert knowledge is typically represented by a set of rules (implications) assigned with weights specifying their (un)certainties. The task of inference mechanism in such rule-based expert systems can be analyzed from the many-valued (fuzzy) logic perspective. On the other hand, implicational relations between two Boolean attributes derived from data (association rules) are quantified in data-mining procedures by [0,1]-valued functions defined on four-fold tables corresponding to pairs of the attributes. In the paper, some theoretical properties connecting these two types of many-valued implications are presented. Obtained results can serve as a basis for an integration of data-mining procedures discovering association rules and rule-based knowledge systems.