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Logic tuple centres have shown that logic-based languages can be effectively exploited not only for building individual agents and enabling inter-agent communication in multi-agent systems, but also for ruling 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 general semantic framework for asynchronous distributed systems allowing a coordination medium to be formally denoted in a separate and independent way with respect to the whole coordinated system. This shows that a logic-based coordination medium does not limit agents and coordination languages to be logic-based, but may instead enable agents of different sorts and technologies to be combined and coordinated in an effective way by exploiting a logic-based approach.