Towards a Formalization of the Unified Modeling Language
  The Unified Modeling Language UML is a language for specifying visualizing and documenting object oriented systems UML combines the concepts of OOA OODOMT and OOSE and is intended as a standard in the domain of object oriented analysis and design Due to the missing formal mathematical foundation of UML the syntax and the semantics of a number of UML constructs are not precisely defined.This paper outlines a proposal for the formal foundation of UML that is based on a mathematical system model 
Ruth Breu, Ursula Hinkel, Christoph Hofmann, Cornel Klein, Barbara   Paech, Bernhard Rumpe, V. Thurner
cs.SE