Causality measures and analysis: A rough set framework

Data and rules power expert systems and intelligent systems. Rules, as a form of knowledge representation, can be acquired by experts or learned from data. The accuracy and precision of knowledge largely determines the success of the systems, which awakens the concern for causality. The ability to elicit cause–effect rules directly from data is key and difficult to any expert systems and intelligent systems. Rough set theory has succeeded in automatically transforming data into knowledge, where data are often presented as an attribute-value table. However, the existing tools in this theory are currently incapable of interpreting counterfactuals and interventions involved in causal analysis. This paper offers an attempt to characterize the cause–effect relationships between attributes in attribute-value tables with intent to overcome existing limitations. First, we establish the main conditions that attributes need to satisfy in order to estimate the causal effects between them, by employing the back-door criterion and the adjustment formula for a directed acyclic graph. In particular, based on the notion of lower approximation, we extend the back-door criterion to an original data table without any graphical structures. We then identify the effects of the interventions and the counterfactual interpretation of causation between attributes in such tables. Through illustrative studies completed for some attribute-value tables, we show the procedure for identifying the causation between attributes and examine whether the dependency of the attributes can describe causality between them.