In NF2 calculus, aggregation as well as selection can be formalised by join and nesting operations. Aggregation must not create new object types. By NF2 nesting operations, new NF2 relation types cannot be created. As a consequence, the detailed conceptual schema must comprise the entire set of aggregate object types that result from subsequent clustering operations. Aggregation must be based on references.
Most studies require aggregations to be based on references.
This operation must be considered as invalid because in the corresponding NF2 schema, no transformation can be defined that yields a relation type that corresponds to the aggregate object type. Object type clustering cannot be performed algorithmically. Therefore, the utilisation of algorithms is limited to the validation of clustering decisions that have been proposed by a developer. One the one hand, most studies do not allow to aggregate a semantically weak object type into more than one dominant object type. But it is generally accepted that conceptual schemata are nets and not trees.