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Triple space computing is a communication and coordination paradigm that allows communication of semantic technologies in general, by publish and read of semantic data. It has also been provided as an underline communication middleware for semantic Web services. While focusing on scalability and openness of triple space computing to bring it into its full potential in a global view, the possibility of heterogeneity among different users communicating over triple space is very likely to arise. This paper focuses on providing the triple space computing with data mediation to enable easy integration of data, information, and knowledge. Mediation is a technique to overcome heterogeneity issues in a system, i.e. to remove differences in the syntactic representation and the intended semantics of data that is exchanged . The paper introduces an abstract mapping language and shows how mapping rules can be created using this mapping language. It further proposes mediation APIs for users and internal system. It also explains the grounding of mediation mapping rules to triple space. It further provides a refined version of architecture of the mediation engine along with its bindings with other components of triple space computing paradigm.