On semantic propagation mechanism in aggregate relationship

In aggregate relation, there are semantic propagations between whole object and part object because the whole object manages and controls the part object. So, based on the lifetime of object, semantic propagations of creating and destroying operation between whole object and part object are clarified in the paper. On the other hand, semantic propagations of the other operations in aggregate relation are also discussed. However, UML only represents aggregate and composition without representing the semantic propagations in aggregate relation. In order to describe real world clearly and correctly, UML is extended for theirs visual expression and theirs formalization in algebraic theory is presented.