Logic-based languages have already proved to be effective to build individual agents and to enable inter-agent communication in multi-agent systems. Also, logic tuple centres have shown that logic-based languages can be effectively exploited to rule inter-agent communication so as to build social behaviours. In this paper, we formally define the notion of logic tuple centre as well as the operational semantics of the logic-based language ReSpecT for the behaviour specification of logic tuple centres. For this purpose, we exploit a formal framework for asynchronous systems allowing coordination media to be represented in a separate and independent way with respect to the coordinated entities. As a by-product, this shows that a logic-based approach may be effectively exploited for the coordination of heterogeneous agents of different sorts and technologies.