UML static models in formal approach

The semantics of models written in UML is not precisely defined. Thus, it is hard to determine, how a given change in a model influences its meaning and, for example, to verify whether a given model transformation preserves the semantics of the model or not. In the paper a formal (mathematical) semantics of key elements of the UML static models is presented. The aim is to define the basic semantic relations between models: a consequence (implication) and equivalence. The goal of the definitions and examples presented in the article is to form a very basic, concise, theoretical foundation for the formal comparison of the UML static models, based on their meanings.