One of the most influential theories of questions, Hamblin's (Hamblin, 1973) emerged as a consequence of Hamblin's earlier work on conversational relevance in the dialogue games of scholastic logic. Hamblin can be understood as proposing his interrogative denotations as a means for operationalizing relevance (in the sense of *conversational coherence*) :
        (H) p is relevant as a response to q if p ∈ q.
In what follows, I restrict attention to relevance relating a query to a possible response. The interrogative denotations Hamblin proposed seem to provide sufficient conditions for relevance. But they fall far short of providing necessary conditions, as in the examples in (1a-d) and (2a-c).

(1) Carla: Are you voting for Tory?
   (a) Denise: I might.
   (b) Denise: Tory?
   (c) Denise: I don't know.
   (d) Denise: What voting system is in use?

(2) Rhiannon: How much tape have you used up?
   (a) Chris: About half of one side.
   (b) Chris: Not much.
   (c) Chris: What do you mean "used up"?

Some of the cases which fall outwith Hamblin's characterization point, arguably, to a deficiency in his semantic treatment of interrogatives (e.g. (1a) and (2a,b)). But the other cases suggest that, while a theory of interrogatives has a role to play in characterizing relevance, it cannot do the job on its own. Studying the notion of relevance does not seem to require justification—it is a fundamental component of a theory of conversational interaction. Nonetheless, one issue to consider is whether there really is a need for a single notion of relevance, internalized in some way within the semantics. Or whether it is merely a derivative, metatheoretical notion that emerges piecemeal from various coherence relations that a system of dialogue semantics provides (this seems to be the view implicit in Asher and Lascarides, 2003, for instance.).

There is at one substantive argument for internalizing relevance, as well as some methodological motivation. The substantive argument is that a unitary notion of conversational relevance seems to underpin both certain types of clarification questions (questions seeking clarification of the relevance of a prior utterance) and certain types of inferences, the latter first described by Grice as flouting the maxim of relevance:

(3) (a) Marjorie:Don't touch that cos she hasn't had it yet.
          Dorothy:Does she eat anything?
          Marjorie:What do you mean?
     (b) A: Horrible talk by Rozzo.
          B: It's very hot in here.
      (Inference: B does not wish to discuss A's utterance.)

The methodological argument is that characterizing relevance pushes theories of interrogatives to be concrete, forcing them to be precise about the range of propositions they characterize as answers and to offer sources of relevance to utterances whose relevance as an answer they do not underpin.

In this paper I propose an account of relevance with the dialogue theory KoS (Ginzburg, 1996, forthcoming, Larsson, 2002, Purver, 2004, Fernandez, 2006). The account is formalized in Type Theory with Records (Cooper, 2005). I start by discussing relevance that is derived directly from interrogative semantics—this includes both answerhood and the relation of dependence between questions. I then consider metacommunicative relevance—this is a notion that holds between an utterance and propositions and questions, respectively, that acknowledge the utterance as understandable or seek clarification about the utterance. Metacommunicative relevance makes us realize that relevance is, in general, a notion that cannot be defined in purely semantic terms (i.e. at the level of content), but requires us to bring utterances—speech events into the picture. I will also consider briefly two more types of relevance, metadiscursive relevance (a notion that underwrites utterances like "I don't know" and "I don't want to talk about this.") and genre-based relevance, the latter much studied in AI work on dialogue.

Finally I will try to combine the various notions of relevance so that they can be used to explicate examples of the type (3) above. I hope also to be able to provide results of a pilot corpus study that shows that this notion of relevance achieves high rates of success in classifying responses to queries.