A Logical Formulation of the Granular Data Model

In data mining problems, data is usually provided in the form of data tables. To represent knowledge discovered from data tables, decision logic (DL) is proposed in rough set theory. While DL is an instance of propositional logic, we can also describe data tables by other logical formalisms. In this paper, we use a kind of many-sorted logic, called attribute value-sorted logic, to study association rule mining from the perspective of granular computing. By using a logical formulation, it is easy to show that patterns are properties of classes of isomorphic data tables. We also show that a granular data model can act as a canonical model of a class of isomorphic data tables. Consequently, association rule mining can be restricted to such granular data models.