Turn-taking with a hidden agenda

We propose a simple model of turn-taking in an information state based approach to dialogue using TTR (Type Theory with Records). The information state (dialogue gameboard) contains an agenda formulated as a list of speech event types that the dialogue participant plans to realize. A novel aspect of the proposal is that the agenda also includes types of events that intuitively should be carried out by an interlocutor. We argue that all dialogue events should be regarded as events jointly carried out by the dialogue participants and that this yields a simple formal method for representing turn-taking in a formal treatment of dialogue. 1 Perception and types In the literature on TTR (Type Theory with Records), see Cooper and Ginzburg (2015) for a recent introduction, a connection is made between the notion of judgement in type theory (judging that an object or event is of a certain type) and perception, that is, perception involves classifying something as being of a certain type. We will describe this in this section. As we interact with our environment we not only perceive objects but also create new objects of certain types. Performing an action is creating an event of a particular type. A plan is a list of types which we hope to realize in this way. Thus we obtain a simple theory of action based on type theoretic ideas, which we will describe in Section 2. In Section 3 we will consider how coordinated action can be modelled in terms of games in this framework. We will see in Section 4 that this type theoretical view of action leads naturally to a notion of joint action and that this is important in order to obtain a theory of coordinated action. Finally, in Section 5, we will apply this view of action to turn taking in dialogue. TTR is a type theory which takes many ideas from Martin-Löf type theory (Martin-Löf, 1984; Nordström et al., 1990). This kind of type theory differs from the version of the simple theory of types that Montague used (Montague, 1973; Montague, 1974) in that it allows for a rich collection of types including types like Dog and, following a suggestion by Ranta (1994), types of situations like A boy hug a dog in addition to the kind of types corresponding to basic ontological categories (for example, in Montague’s case, types like Entity and Truth value) and all types of functions based on the basic types which are introduced in simple type theory. Central to this kind of type theory is the notion of a judgement that an object a is of a type T , in symbols, a : T . We will sometimes refer to a as a witness for the type T . In the literature on TTR this notion of judgement is connected to a theory of perception. An act of perception involves making such a type judgement. When we perceive something we perceive it as being of a certain type. That is, perceiving an object a as a dog involves making the type judgement a : Dog. Similarly perceiving a situation, e, as one in which a boy hugs a dog involves making the type judgement e : A boy hug a dog. Agents are thought of as having a collection of types available as a resource which they can employ in, among other things, acts of perception. The types available to an agent are in part limited by their perceptual apparatus.