Web Service Composition creates new composite Web Services from the collection of existing ones to be composed further and embodies the added values and potential usages of Web Services. Web Service Composition includes two aspects: Web Service orchestration denoting a workflow-like composition pattern and Web Service choreography which represents an aggregate composition pattern. There were only a few works which give orchestration and choreography a relationship. In this paper, we introduce an architecture of Web Service Composition runtime which establishes a natural relationship between orchestration and choreography through a deep analysis of the two ones. Then we use an actor-based approach to design a language called AB-WSCL to support such an architecture. To give AB-WSCL a firmly theoretic foundation, we establish the formal semantics of AB-WSCL based on concurrent rewriting theory for actors. Conclusions that well defined relationships exist among the components of AB-WSCL using a notation of Compositionality is drawn based on semantics analysis. Our works can be bases of a modeling language, simulation tools, verification tools of Web Service Composition at design time, and also a Web Service Composition runtime with correctness analysis support itself.