Giving a formal semantic to an UML Activity diagram (UML AD) is a hard task. The reason of this difficulty is the ambiguity and the absence of a precise formal semantic of such semi-formal formalism. A variety of semantics exist in the literature having tackled the aspects covered by this language. We can give as example denotational, functional and compositional semantics. To cope with the recent tendency which gave a heterogeneous semantic to UML diagrams, we aim to define an algebraic presentation of the semantic of UML AD. In this work, we define a formal semantic of UML 2.0 AD based on institution theory. For UML AD formalism, which is a graphical language, no precise formal semantic is given to it. We use the institution theory to define the intended semantic. Thus, the UML AD formalism will be defined in its own natural semantic.
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