Overview

This course will present an approach to linguistic communication using TTR, a type theory with records. It will provide a basic introduction to TTR including formal techniques and the use of types to analyse perception, mental states and attitudes likes belief. It will show how meaning can be grounded by relating types to perceptual classifiers. It will propose a general theory of action based on types and show how linguistic communication can be embedded in this theory. The emphasis will be on a hands-on approach where participants will be encouraged to work through examples based on exercises.

TTR is a rich type theory building on ideas from Martin-Löf type theory. In contrast to the type theory Montague uses there are not just types for basic ontological categories such as entities and functions which can be constructed on the basis of these but also types of objects like Tree and types of events like boy-hug-dog. Types play the role of propositions, “true” just in case there is something of the type.

We will also model mental states in terms of types. For example, a belief corresponds to a type and the belief is true just in case the type has a witness. Linguistic communication involves the updating of mental states (commonly called information states or gameboards in the dialogue literature) representing an agent's view of the state of the conversation, for example, what questions are under discussion and what commitments are shared between the agent and their interlocutor. Updates are triggered by the perception of speech events of particular types.

In Lecture 1 we will introduce some of the basics of TTR and relate it to the perception of objects and events. A central notion in type theory is that of judgement that an object or event, a, is of type, T, in symbols: a:T. We say that a is a witness for T. Perception of an object or event involves making a type judgement, that is, classifying the object or event to be of a particular type. We will argue during the course that this view of perception lies at the root of much of our linguistic processing and notions of meaning.

Lecture 2 will argue that types can be related to perceptual classifiers as discussed in the psychological and computational literature and will discuss how types can be learned.

Types are intensional in the sense that two distinct types may have exactly the same witnesses. This fact lays the groundwork for a treatment of mental states and attitudes in terms of types which will be discussed in Lecture 3. Among other things, this treatment avoids the problems that arise in classical (Montague) model-theoretic semantics where propositions are treated as the sets of possibles worlds in which they are true. The classical treatment has the consequence that logically equivalent propositions (true in the same possible worlds) are identical.

Lecture 4 will discuss a theory of action related to types. For example, judging an object to be of a type can be seen as one kind of action. Another kind of action is that of creating an object of a type. This is particularly useful when we are considering the realization of an event of a particular type. The lecture will discuss how this can be applied to the notion of information state update in dialogue theory and also to the notion of grammar seen in terms of information state update. For example, the humble phrase structure rule can be seen as an update rule concerning the information state relating to the incremental perception of a linguistic event.

Lecture 5 will discuss pyttr, a Python implementation of some of the core notions discussed in Lectures 1–4.

Participants will be encouraged to do practical exercises on the details of TTR and opportunities will be provided during the course to discuss solutions to these exercises as we progress through the course.