### abstract ###
One of the most utilized data mining tasks is the search for association rules
Association rules represent %probabilistically 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  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
### introduction ###
One of the goals of data mining is to discover interesting relationships from data
Association rules express relationships that hold with sufficient frequency but not always
For example, it may be the case that not all managers earn over \ SYMBOL pq  SYMBOL p SYMBOL q SYMBOL q SYMBOL p SYMBOL p SYMBOL q SYMBOL p SYMBOL q SYMBOL pq SYMBOL p q SYMBOL fr(pq)$
Our definition of frequency for ER queries generalizes previous work on defining association rules in a multi-relational setting
CITATION  discusses extending itemset rules with negations and motivates the usefulness of this extension
The query extension approach of the system  CITATION  presents a special class of entity-relationship rules that allows conjunctions of nonnegated statements and existential quantification
Our concept  of ER rules %allows features in addition negations, universal quantification, nested quantifiers, and nested Boolean combinations
Thus one contribution of this paper is an extended rule format
A characteristic that distinguishes our approach from previous work is that previous approaches assume a given target table that defines a base set of tuples for evaluating the support of a query
In contrast, we start with a query and define a natural base set of tuples for evaluating the support of the query
We can think of this approach as dynamically generating entity sets for a given query rather than evaluating queries with respect to a fixed entity set
Thus the second main contribution of this paper is a new definition of support  for rules in our extended format
The paper is organized as follows
First we review basic relational database concepts such as the relational schema and the domain relational calculus
Then we introduce the concept of an entity query and define the frequency of a query in this class of queries
This definition provides the basis for the notion of an entity-relationship rule and for defining the support of an entity-relationship rule
We compare entity-relationship queries to frequent itemsets and to the rule language of the system
The final section establishes sevveral important formal properties of query frequencies as we define them and shows that they satisfy the Apriori property, that is, the frequency of a conjunction is no greater than the frequency of its conjuncts
