Uwe Mönnich has worked both on the use of type theory in semantics and on formal aspects of grammar formalisms. This paper suggests a way of bringing together type theory and unification as found in

generalised quantifiers and hypothetical contexts

We propose a record type theoretical account of cases of copredication which have motivated the introduction of dot types in the Generative Lexicon (Asher and Pustejovsky, 2005). We will suggest that using record types gives us a simple and intuitive account of dot types and also makes a connection between copredication and the use of hypothetical contexts in a record type theoretic analysis of dynamic generalized quantifiers. We propose a view of lexical innovation which draws both on Pustejovsky’s original work on the Generative Lexicon (Pustejovsky, 1995) and the notion of resource present in the Grammatical Framework (Ranta, forthcoming). 1

We propose a shift in perspective from the view of natural languages as formal languages to natural languages as a collection of resources for constructing local languages for use in particular situations. This is suggested by our experience constructing natural language grammars for particular applications using the Grammatical Framework. It points to a research programme investigating how such resources play a role in linguistic innovation by agents constructing situation-specific local languages and how they can be made dynamic, modified by the linguistic agent’s exposure to innovative linguistic data. 1 Natural languages and formal languages The view of natural languages as formal languages played a significant role in the development of linguistics in the second half of the twentieth century. The view of languages as sets of strings underlay the early development of generative transformational grammar. The following famous quotation from Montague’s (1974) ‘Universal Grammar ’ represents a cornerstone of work on formal semantics since the seventies: ∗ This work was supported by Vetenskapsr˚adet project 2005-4211 Library-based Grammar Engineering,

One of the important challenges facing NL semantics in the early 21st century is to theoretically underpin analysis and generation of conversational interaction. I start by considering certain requirements a semantic framework needs in order to be viable for this task, with reference to a benchmark example. One fundamental requirement is the provision of an ontology which incorporates propositions, questions, and similar abstract entities. The main theme of this paper concerns the construction of such an ontology. I argue that Barwise and Perry’s approach to ontology—including its nonstandard trichotomy distinguishing between situations/events, situation types, and propositions—provides useful building blocks. I implement the construction using the type theoretic framework developed by Cooper (this journal).

Records and record types in semantic theory

Abstract not found

This paper introduces a formal view of the semantics and pragmatics of corrective feedback in dialogues between adults and children. The goal of this research is to give a formal account of language coordination in dialogue, and semantic coordination in particular. Accounting for semantic coordination requires (1) a semantics, i.e. an architecture allowing for dynamic meanings and meaning updates as results of dialogue moves, and (2) a pragmatics, describing the dialogue moves involved in semantic coordination. We illustrate the general approach by applying it to some examples from the literature on corrective feedback, and provide a fairly detailed discussion of one example using TTR (Type Theory with Records) to formalize concepts. TTR provides an analysis of linguistic content which is structured in order to allow modification and similarity metrics, and a framework for describing dialogue moves and resulting updates to linguistic resources. 1

Semantic change happens both in the long term (over years and decades) and in the very short term (in a single dialogue) 1. An exploratory study of a Map Task dialogue indicates that dialogue participants coordinate on an ad-hoc vocabulary and associated concepts (meanings) to enable information exchange, and that adhoc vocabularies can be cobbled together from a heterogeneous mix of “microvocabularies” borrowed from various other (a priori unrelated) domains. To account for these observations, I outline an abstract and general formal account of how the meanings of natural language expressions (typically, words) can change as a result of their use in dialogue. The account has two parts, one semantic and one pragmatic. In the semantics part, a basic framework for formalising updates to semantic systems in dialogue is sketched. In the pragmatics part, semantic updates are related to interactional processes of semantic coordination in dialogue, such as feedback, negotiation and accommodation. 2

We shall consider a formulation of generalised quantifiers using type theory with records (TTR). TTR follows closely the development of record types in Martin-Löf or constructive type theory but differs in that the type theory is defined on a classical set theoretic basis. This means that the classical set-theoretic approach to generalised quantifiers can be imported into the type theoretic framework. The result is, I believe, equivalent to the proposal for dynamic generalised quantifiers in Chierchia (1995). The use of dependent types provides us with an elegant approach to the formulation of dynamic quantifiers. We use a notion of hypothetical context which we have used elsewhere to give accounts of intentional identity, answers to questions and information state updates in dialogue management. We suggest that this points towards a general theory of hypothetical context in natural language. We suspect also that our analysis using records will support analyses of common