In this paper we compare three different formalisms that can be used in the area of models for distributed, concurrent and mobile systems. In particular we analyze the relationships between a process calculus, the Fusion Calculus, graph transformations in the Synchronized Hyperedge Replacement with Hoare synchronization (HSHR) approach and logic programming. We present a translation from Fusion Calculus into HSHR (whereas Fusion Calculus uses Milner synchronization) and prove a correspondence between the reduction semantics of Fusion Calculus and HSHR transitions. We also present a mapping from HSHR into a transactional version of logic programming and prove that there is a full correspondence between the two formalisms. The resulting mapping from Fusion Calculus to logic programming is interesting since it shows the tight analogies between the two formalisms, in particular for handling name generation and mobility. The intermediate step in terms of HSHR is convenient since graph transformations allow for multiple, remote synchronizations, as required by Fusion Calculus semantics.