Association Rules in the Relational Calculus

One of the most utilized data mining tasks is the search for association rules. Association rules represent significant relationships between items in transactions. We extend the concept of association rule to represent a much broader class of associations, which we refer to as \emph{entity-relationship rules.} Semantically, entity-relationship rules express associations between properties of related objects. Syntactically, these rules are based on a broad subclass of safe domain relational calculus queries. We propose a new definition of support and confidence for entity-relationship rules and for the frequency of entity-relationship queries. We prove that the definition of frequency satisfies standard probability axioms and the Apriori property.

💡 Research Summary

The paper tackles a fundamental limitation of classic association‑rule mining, which traditionally assumes a flat “item‑transaction” model and therefore cannot express relationships that span multiple tables or involve complex object attributes. To overcome this, the authors introduce entity‑relationship (ER) rules, a formalism that captures associations between properties of related objects in a relational database.

An ER rule consists of an antecedent and a consequent, each expressed as a query in a safe subset of the domain relational calculus (DR‑C). Safety guarantees that every free variable is bound to a finite domain, ensuring that query results are computable on a real database. By grounding rules in DR‑C, the authors obtain a precise logical syntax that can describe arbitrary joins, selections, and projections while remaining decidable.

The central technical contribution is a new definition of support and confidence for ER rules. Instead of counting transactions, the authors define the frequency of a DR‑C query Q as

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