In this paper we propose a computational model for human-agent and agent-agent conversation. This model has two fundamental characteristics: (1) it takes into account the implicit aspects of conversations by dealing with the non literal level of speech acts; (2) it models the dialogization process. Theoretically, our model uses a public approach based on social commitments and on what we call communicational states. In addition, we consider communication as a negotiation process formed by a set of initiative/reactive dialogue games. The paper also presents an implementation of our model in a multi-agent system called POSTAGE.