Association Rules in the Relational Calculus

TL;DR

This paper extends traditional association rules to entity-relationship rules within relational calculus, enabling broader and more semantically meaningful data associations with proven probabilistic properties.

Contribution

It introduces a new class of association rules based on safe domain relational calculus queries, along with definitions of support and confidence that satisfy probability axioms and the Apriori property.

Findings

Support and confidence definitions satisfy probability axioms.

Frequency of entity-relationship queries adheres to the Apriori property.

Broader class of association rules enhances data mining capabilities.

Abstract

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.