This article presents semantic-based composition of processes of Semantic Web Services using predetermined semantic descriptions of the services. Currently most proposed techniques are syntactically, rather than semantically, oriented. Our proposed method involves a semantic-based composition agent which is called Semantic Composition Agent (SCA). The novel design of SCA applies two different well-known approaches, namely Process Algebra and Armstrong Axioms, in its two major components (planner and inference engine respectively) of the process composition framework. In order to demonstrate its applicability, a prototype of SCA was implemented and tested against a number of Web services composition cases.