A major critique against BDI (Belief, Desire, Intention) approaches to the communication is that they require strong hypotheses such as sincerity, cooperation... on the mental states of the agents (cf. for example [Singh, 1998; Singh, 2000; Fornara & Colombetti, 2002]). The aim of this paper is to give an operator remeding this defect to a logic BDI. Thus we study communication between heterogeneous agents via the notion of ''grounding'', in the sense of being publicly expressed and established. We show that this notion is different from social commitment, from the standard mental attitudes, and from different versions of common belief. Our notion is founded on speech act theory, and it is directly related to the ''expression of the sincerity condition'' [Searle, 1969; Searle, 1983; Vanderveken, 1991] when a speech act is performed. We use this notion to characterize speech acts in terms of preconditions and effects. As an example we show how persuasion dialogues ''à la Walton & Krabbe'' can be analyzed in our framework. In particular we show how speech act preconditions constrain the possible sequences of speech acts.