The question of relevance is fundamental, and goes far beyond the mere study of conversation. Living beings are equipped to detect what in their environment may be relevant to their survival or to the survival of their offspring. Any sign or action is or is not relevant at a given moment, even when communication is not intended. And no intended communication can proceed if communicants have no way to decide whether and how what they receive is relevant, and if they have no procedure to produce signs that will be perceived as relevant. Verbal communication seems to be the main distinctive feature that makes us different from animals. It is a wonder that we still have no precise idea of how we detect and produce relevant utterances !
One of the main aims of research in Pragmatics, in our view, is to determine a list of constraints that limit options of interlocutors during verbal interaction. If anything could be said, there would be no Pragmatics ! Such constraints, that limit the content of what can be said, are constraints of relevance. At a given moment of an interaction, everybody knows that the range of options for the next speaker, though wide, is dramatically limited compared to what may be thought of. A very good indicator of such limits is the existence of breakdowns (like "What do you say that ?", or "So what ?"). They suggest that some constraint of relevance has been violated for one reason or another (e.g. after a misunderstanding).
Classical theoretical Pragmatics say little about what the content of a relevant utterance should be. Grice's maxim [Grice 1975] is simply " be relevant ", and gives no indication about how. The work of D. Sperber and D. Wilson [1986] goes further in this respect. They first notice that the speaker, as soon as one has recognized his intention to communicate, cannot avoid being expected to be relevant. Thus the relevance expectation does not result from the fact that the speaker is ready to cooperate, as Grice's maxim suggests, but from the fact that (s)he is ready to communicate. Then what makes this expectation satisfied ? According to Sperber and Wilson, a statement is relevant if : (1) it is not in flagrant contradiction with previous knowledge ; (2) new statements can be inferred from it ; (3) such inferences are not too " expensive " in terms of cognitive load. What is spontaneously expected from any person intending to communicate is that the message (s)he delivers matches the hearer's capabilities to make such inferences.
We will suggest here that these constraints on relevance are much too permissive, and that they do not allow much prediction about the content of utterances. Furthermore, requirement (1) will be strongly put into question. Requirements (2) and (3) are by nature gradual. Our own criteria for relevance will be essentially qualitative.
We will first show that from the very beginning, when a new topic is introduced, conversations are constrained. To be perceived as relevant, a new topic must appear as problematic : either paradoxical, or improbable, or highly desirable or undesirable. We will make use of a simple logical formalism to give a unified description of this phenomenon.
We will then show what kind of effects successive replies may have on this problematic topic. Only a few possibilities are offered by our model of relevance : invalidations, "banalization" and "antagonistic" reactions. All of them tend to make the topic less problematic.
We will finally discuss the validity of these results, and mention possible technical applications.