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There are several well-known problem areas in UML (Version 1.3). Although many of these have been reported to the OMG's Revisionary Task Force (RTF), that venue is highly pragmatic; the author considers the detailed "theory" relating to these problem areas. He first discusses the widely used concept of stereotypes and then concentrates on the metamodel for: WP relationships; responsibilities; and Type/Interface/Class. In addition, he identifies areas of the metamodel where UML has been used inexpertly, particularly in the incorporation of generalization to incorrectly represent implementation inheritance relationships and the use of black diamond composition for relationships that are poorly argued to be whole-part relationships. Other issues discussed include the default directionality of associations; the relationship of an association to a dependency; and the general observation that the UML uses a notation that supports expressibility but is not in itself expressive.
Brian Henderson‐Sellers (Mon,) studied this question.