Abstract  The formal methods for security protocols guarantee the security properties of protocols. Instantiation Space Logic is a new security protocol logic, which has a strong expressive power. Compositional Logic is also a useful security protocol logic. This paper analyzes the relationship between these two logics, and interprets the semantics of Compositional Logic in Instantiation Space model. Through our work, the interpreted Compositional Logic can be extended more easily. Moreover, those security protocols described in Compositional Logic can be automatically verified by the verifier of Instantiation Space. The paper also proves that the expressive power of Instantiation Space Logic, which can not be completely interpreted by Compositional Logic, is stronger than Compositional Logic.