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.
The third category of works uses this theory for a specific intention and a precise case study. The work in @cite_6 is a good candidate in this category where authors defined a heterogeneous framework of services oriented system, using institution theory. Authors (in @cite_6 ) aims to define a heterogeneous specification approach for service-oriented architecture (SOA). The developed framework consists of a several individual services specification written in a local logic. The specification of their interactions is written in a global logic. The two defined logics are described via institution theory and an institution comorphism is used to link the two defined institution. This approach is inspired by the work of Mossakowski. Another work is developed in @cite_5 where the authors propose to use institution to represent the logics underling OWL and Z. Then, they propose a formal semantic for the transformation of OWL to Z specification via the use of institution comorphism.
@cite_5 @cite_6
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Checking for properties of Web ontologies is important for the development of reliable Semantic Web systems. Software specification and verification tools can be used to complement the Knowledge Representation tools in reasoning about Semantic Web. The key to this approach is to develop sound transformation techniques from Web ontology to software specifications so that the associated verification tools can be applied to check the transformed specification models. Our previous work has demonstrated a practical approach to translating Web ontologies to Z specifications. However, from a sound engineering point of view, the translation is lacking the theoretical work that can formally relate the respective underlying logical systems of OWL and Z. In this paper, we take the advantage that the logics underlying OWL and Z can be represented as institutions and we show that the institution comorphism provides a formal semantic foundation for the transformation from OWL to Z. Service-oriented architecture (SOA) is a relatively new approach to software system development. It divides system functionality to independent, loosely coupled, interoperable services. In this paper we propose a new heterogeneous specification approach for SOA systems where a heterogeneous structured specification consists of a number of specifications of individual services written in a "local" logic and where the specification of their interactions is separately described in a "global" logic. A main feature of our global logic is the possibility of describing the dynamic change of service communications over time. Our approach is based on the theory of institutions: we show that both logics form institutions and that these institutions are connected by an institution comorphism. We illustrate our approach by a simple scenario of an e-university management system and show the power of the heterogeneous specification approach by a compositional refinement of the scenario.