Intelligent and autonomous software agents may engage in dialogue and argument with one another, and much recent research has considered protocols, architectures and frameworks for this. Just as with human dialogues, such agent dialogues may be facilitated by the presence of a mediator, able to summarise different positions, identify common assumptions and inconsistencies, and make appropriate interventions in the dialogue. Drawing on the theory of co-ordination artifacts in multi-agent systems, we propose a formal framework to explicitly represent the functions of a mediator artifact. We then describe an implementation of this framework using the TuCSoN coordination infrastructure for MAS, where the mediator artifact is realised by a tuple centre—a programmable tuple space.