Introduction

As we interact with the world and with each other we need to classify objects and situations; that is, we need to make judgements about what types of objects and situations we are confronted with. This is an important part of what is involved in planning the future actions we should carry out and how we should coordinate with other agents in carrying out collaborative actions. This is true of action in general, including linguistic action. This classification needs to be multimodal in that we need to classify what we experience through different senses and be able to combine the information in order to come to a judgement. The aim of this book is to characterize a notion of type which will cover both linguistic and non-linguistic action and to lay the foundations for a theory of action based on these types. We will argue that a theory of language based on action allows us to take a perspective on linguistic content which is centred on interaction in dialogue and that this is importantly different to the traditional view of natural languages as being essentially similar to formal languages such as logics developed by philosophers or mathematicians. At the same time we will argue that the tremendous technical advances made by the formal language view of semantics can be incorporated into the action-based view and that this can lead to important improvements both of intuitive understanding and empirical coverage. In this enterprise we use types rather than possible worlds as commonly employed in studies of the semantics of natural language. Types are more tractable than possible worlds and give us more hope of understanding the implementation of semantics both on machines and in biological brains. Part I of the book (Chapters 1–3) deals with a theory of types related to perception and action and shows a way of presenting a theory of grammar within a theory of action. Part II (Chapters 4–8) then looks at a number of central issues in semantics from a dialogical point of view and argues that there are advantages to looking at some old puzzles from this perspective. In Chapter 1 we introduce a notion of perception of an object or situation as making a judgement that it is of a type. In symbols, we write a:T to indicate that a is of type T. We shall talk interchangeably of something being of a type or being a witness for a type. Our claim is that perceiving something involves classifying it as being of a type, even if that type is very general (like PhysicalObject or Event)—we cannot perceive it simpliciter. Following Kant we cannot perceive das Ding an sich (“the thing itself”) but only in terms of a type that we assign to it. We present basic notions of the theory of types which will be developed in the book, TTR, a theory of types with records, which builds to a great extent on ideas taken from the type theory of Per Martin-Löf although we have made significant changes both in the general design and aims of the theory and a number of details which appear to us to be motivated by cognitive and linguistic considerations. The overall approach presented here owes much to the theory of situations and situation semantics presented by Barwise and Perry in the 1980s. One of the themes of this book is a working out of parts of the old situation theory using ideas taken from Martin-Löf’s type theory. A central notion in TTR is that of record. The term “record” is used in computer science for what is often called an attribute-value matrix (AVM) or feature structure in linguistics. A record is a collection of fields consisting of a label (attribute or feature in the standard linguistic way of talking) and an object of some kind (which itself can be a record). A schematic example of a record is given in (1), where the ℓi are labels and the oi are objects (including situations). (1) Records are witnesses for record types which are also collections of fields. Rather than objects, the fields in a record type contain types. In the schematic example in (2) the Ti are types. (2) The record (1) will be of the type (2) just in case the objects are of the types with the same labelling, that is, o0:T0⁠, o1:T1 and o2:T2⁠. Martin-Löf’s orginal type theory did not have records or record types though there have been many suggestions in the literature on how to add them. We have borrowed freely from some of these ideas in TTR although the way we have developed the notions differs essentially from previous proposals. We will use records and record types to model situations and situation types in a sense related to that of situation semantics as developed by Barwise and Perry. The records and record types are also related to discourse representation structures as introduced by Kamp. In Chapter 2 we introduce some basic notions of a theory of action based on these types which will be developed further as the book progresses and apply the theory of types from Chapter 1 to basic notions of information update in dialogue. Here we build on seminal work on dialogue analysis by Jonathan Ginzburg and also related computational implementation by Staffan Larsson leading to the information state update approach to dialogue systems. We have adapted these ideas in a way that allows us to pursue the questions of grammar and semantics that we take up in the remainder of the book. A central notion here is that of the dialogue gameboard which we construe as a type of information state representing the current state of play in the dialogue from the perspective of a dialogue participant. It includes the dialogue participant’s view of what has been committed to as being true in the dialogue so far and what questions are currently under discussion. In Chapter 3 we show how syntax and semantics can be embedded in the theory of action characterized in Chapters 1 and 2. Grammatical rules are regarded in terms of affordances which license us to draw conclusions about the types to be associated with speech events on the basis of speech events previously perceived. This is in contrast to a formal language view where language is seen as a set of analysed strings of symbols associated with meanings of some kind. The philosophical ground of the action-based approach goes back to the relational theory of meaning introduced in Barwise and Perry’s situation semantics which focusses on the relation between utterance situations and described situations. This was perhaps the first attempt to generalize the Speech Act Theory developed by Austin and Searle to the concerns of compositional interpretation of syntactic structure. It also enables us to develop a formal approach to dialogical theories of language such as those developed by the psychologist Herb Clark and the linguist Per Linell. A recent theory to which the ideas in this chapter are related is that of Dynamic Syntax (DS). While the particular formulations in our approach look rather different from those in DS, the two theories have common aims relating to the analysis of language as action and an emphasis on the incremental nature of language which in this chapter we relate to the building of a chart type. There is also a common interest in the treatment of language as a system in flux where an act of speaking can create a new previously unavailable linguistic resource that can be reused in future speech events. Thinking of grammar in terms of a theory of action leads us into an approach to syntax and semantics which emphasizes how we reason about speech events and their types. This relates to several strands in linguistic analysis which emphasize the inferential nature of syntactic and semantic processing including Pereira and Warren’s parsing as deduction, various kinds of categorial grammar including Morrill’s Type Logical Grammar and glue semantics as used in Lexical Functional Grammar (LFG) by Dalrymple and others. Of particular importance is Aarne Ranta’s work on Type-Theoretical Grammar and the Grammatical Framework. The use of records and record types and their similarity to typed feature structures makes the notion of grammar here closely related to that of Head Driven Phrase Structure Grammar (HPSG). The theory of types that we employ gives us two notions which will be important in the development of semantics in Part II. The first is the notion of intensionality. Types in TTR are intensional in that the identity of a type is not established in terms of the set of witnesses of that type. That is, types are not extensional in the way that sets are in a standard set theory. The axiom of extensionality in standard set theory requires that there cannot be two sets which have the same members. In contrast, there can be different types which have exactly the same set of witnesses. The second notion has to do with the facts that the types themselves are treated as objects that can enter into relations and be used to construct new types. We will call this first class citizenship of types, though it is related to notions of intentionality (with a “t”) and reflection in programming languages, that is, the ability not only to carry out procedures but to reflect on and reason about them. In our terms, an important enabling factor for human language is that we not only can perceive objects and situations in terms of types and act on these perceptions but that we can also reason about and act on the types themselves, for example, in ascribing them to other agents as beliefs or making a plan to achieve a goal by creating an event of a certain type. The types become cognitive resources which we can exploit in our communicative activity. In Part II we will look at a number of examples of this. In Chapter 4 we examine reference by uses of proper names and occurrences of pronouns which are not bound by quantifiers. In order to account for this we need a notion of parametric content, which is to say that the content of an utterance depends on a context belonging to a certain type. For example, an utterance of the proper name Sam requires a context in which there is an individual named “Sam”. But where in her resources should a dialogue participant look for such a context? One obvious place is the conversational gameboard that we introduced in Chapter 2. That is, the dialogue participant should determine whether there has been reference to somebody of that name already in the current dialogue according to her gameboard. Another place is the visual scene, or more generally the ambient situation which the agent can perceive by different sense modalities. This we also represent as a resource using a type—that is, the type for which the ambient situation would be a witness if the agent’s perception is correct. Yet another place to look is the agent’s long-term memory (which we will equate with the agent’s beliefs, although one may ultimately wish to make a distinction). This resource is also modelled as a type representing how the world would be if the agent’s memory or beliefs are correct. (The structured nature of record types means that they can be used in effect as large repositories of information indexed by the paths provided by the labels in the record type.) The fact that we are reasoning about the extent to which the context type associated with the utterance matches the types modelling the agent’s relevant resources enables us to talk about cases where there are names of non-existent objects (that is, the agent’s resource types do not exactly match the world) or where a single object in the world corresponds to two objects in the resources or vice versa (another way in which there can be a mismatch between reality and an agent’s resources). The proposal to represent different aspects of mental states in terms of record types is closely related to (and inspired by) similar proposals for representing mental states using discourse representation structures. In Chapter 5 we look at frames associated with common nouns. (The restriction to common nouns here has to do with the examples that will be discussed and is not a claim that only common nouns are associated with the kinds of frames we propose.) The idea of frames goes back to early work on frame semantics by Fillmore and also psychological work on frames by Barsalou. We will construe frames as situations (modelled as records in TTR). We will argue that frame types are an additional kind of resource which is exploited in natural language semantics. A common noun like dog, in addition to being associated with the property of being a dog (that is, a simple property characterized in terms of the single predicate ‘dog’), can also be associated with a type of situation (a frame type) which is common for dogs, for example, where the dog has a name, an age and various other attributes we commonly attribute to dogs. We will argue that such a frame can play an important role in interpreting utterances such as the dog is nine in the sense of “the dog is nine years old”. Some nouns, such as temperature, seem to represent frame level predicates, following an analysis suggested by Sebastian Löbner in order to account for the analysis of utterances like the temperature is rising where it is not the case that some particular temperature is rising (say, 30∘⁠) but that different situations (frames) with different temperatures are being compared. Nouns which normally predicate of individuals can be coerced to predicate of frames. An example is the noun ship in an example originally discussed by Manfred Krifka: four thousand ships passed through the lock which can either mean that four thousand distinct ships passed through the lock or that there were four thousand ship-passing-through-the-lock events some of which may have involved the same ship. We argue that in order to interpret such examples you need to have as a resource an appropriate frame type associated with the noun ship. In Chapter 6 we explore phenomena in natural language which are standardly referred to as modal and intensional. We argue that types as we conceive them are better placed to deal with these phenomena than the possible worlds that are used in standard formal semantics. In standard formal semantics propositions are regarded as sets of possible worlds. For example, the proposition corresponding to a boy hugged a dog is the set of all logically possible worlds in which a boy hugged a dog is true. What we substitute for this is the type of situations in which a boy hugged a dog. At an intuitive level these notions are quite similar. They both represent mathematical objects which allow for many different possibilities as long as the fact that a boy hugged a dog is held constant across them. One important difference is that sets of possible worlds are extensional sets whereas our types are intensional. Thus it is possible for us to have two distinct types which have exactly the same witnesses. One pair of such examples we discuss is Kim sold Syntactic Structures to Sam and Sam bought Syntactic Structures from Kim. Intuitively we want these to represent different propositions and we argue that they can yield different truth conditions when embedded under a predicate like legal. (Under Swedish law, for example, it is illegal to buy sex but legal to sell sex.) Another pair involves so-called mathematical propositions which are true in all possible worlds but which nevertheless we would want to represent different propositions: Two plus two equals four and Fermat’s last theorem is true (as proved by Andrew Wiles). The chapter begins with a discussion of the problems associated with possible worlds analyses. We then continue with a discussion of modality and in particular of how Angelika Kratzer’s notions of conversational background and ideals can be seen as resources based on types and the kind of topoi that Ellen Breitholtz has introduced in the TTR literature. In the third part of the chapter we discuss what are traditionally regarded as intensional constructions involving attitude verbs like believe and intensional verbs like need and want. We treat ‘believe’ as a relation between individuals and types (corresponding to the content of the embedded sentence). For an individual to believe a type it has to be the case that the type matches (in a way we make precise) the type which models the beliefs (or long-term memory) of the individual, that is the same resource that was needed in Chapter 4 to get the dialogical analysis of proper names to work out. In Chapter 7 we look at generalized quantifiers from the perspective of dialogic interaction. Traditionally generalized quantifiers are treated as sets of sets or sets of properties and the work of Barwise and Cooper on generalized quantifiers built on this idea. Barwise and Cooper also introduced the auxiliary notion of witness set for quantifiers under the heading “Processing quantified statements”. In this chapter we turn things around and make the characterization of witness sets the primary notion in defining quantifiers. This makes it more straightforward to account for the anaphoric possibilities relating to quantified expressions in dialogue. We often use quantified statements in dialogue when we have inadequate information to determine their truth. This is particularly true of determiners like every and most when talking about large sets. We suggest that this phenomenon can be analysed by estimating a probability based on the evidence presented in our cognitive resources (long-term memory or beliefs as discussed in Chapters 4 and 6). In Chapter 8 we give an account of how TTR types can be used to talk of content which is underspecified. The idea is to exploit the notion of types which can have several witnesses as “underspecifications” of those witnesses. Rather than associating contents with utterances as we have done in the earlier chapters, we associate types of contents with utterances. Thus a dialogue participant when observing a speech event associates it with a type of content rather than a particular content. We show how earlier ideas about the treatment of underspecification of quantifier scope and anaphora can be accommodated in this view.