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Object Relationship Notation (ORN) is a declarative scheme that allows a variety of common relationship types to be conveniently specified to a database management system (DBMS), thereby allowing their semantics to be automatically enforced by the DBMS. ORN can be integrated into any data model that represents binary associations or DBMS that implements them. We give a brief description of ORN syntax and semantics and provide algorithms that can be used to implement ORN. These algorithms must deal with the presence of association cycles in the database. We explore in detail the problems caused by such cycles and how ORN and its implementation deal with them, and we show that ORN semantics are noncircular and unambiguous.