Deciding Entailment of Implications with Support and Confidence in Polynomial Space

Association Rules are a basic concept of data mining. They are, however, not understood as logical objects which can be used for reasoning. The purpose of this paper is to investigate a model based semantic for implications with certain constraints on their support and confidence in relational data, which then resemble association rules, and to present a possibility to decide entailment for them.

💡 Research Summary

The paper investigates a logical treatment of association rules by embedding them into the formal concept analysis (FCA) framework and introducing “constrained implications” – implications equipped with quantitative thresholds for support and confidence. A constrained implication is a triple (A → B, s, c) where A and B are attribute sets, s is a minimum support, and c is a minimum confidence, both rational numbers in