This paper embeds the core part of Discourse Representation Theory in the classical theory of types plus a few simple axioms that allow the theory to express key facts about variables and assignments on the object level of the logic. It is shown how the embedding can be used to combine core analyses of natural language phenomena in Discourse Representation Theory with analyses that can be obtained in Montague Semantics.

Preface This book is about semantics and logic. More specifically, it is about the semantics and logic of natural language; and, even more specifically than ...

We provide first-order axioms for the theories of finite trees with bounded branching and finite trees with arbitrary (finite) branching. The signature is chosen to express, in a natural way, those properties of trees most relevant to linguistic theories. These axioms provide a foundation for results in linguistics that are based on reasoning formally about such properties. We include some observations on the expressive power of these theories relative to traditional language complexity classes.

The format of this book is unusual, especially for a book about linguistics. The book is meant primarily as a research monograph aimed at linguists who have some background in formal semantics, e. g. Montague Grammar. However, I have two other audiences in mind. Linguists who have little or no experience of formal semantics, but who have worked through a basic mathematics for linguists course (e. g. using Wall, 1972, or Partee, 1978), should, perhaps with the help of a sympathetic (...) Montague gramma rian, be able to discover enough of how I have adapted some of the basic ideas in formal semantics to make the developments that I undertake in the rest of the book accessible. Logicians and computer scientists who know about model theoretic semantics and formal systems should be able to glean enough from Chapters I and II about linguistic concerns and techniques to be able to read the remainder of the book, again possibly with the help of a sympathetic Montague grammarian. However, readers should beware. Chapter II is not meant as a general introduction either to formal semantics or to linguistics and while much of the presentation there is going over ground that is already well covered in the literature, the particular formulation and the emphases are very much oriented to the developments to be undertaken later in the book. (shrink)

I reject the contention that an important theoretical difference exists between formal and natural languages.

Ambiguities in natural language can multiply so fast that no person or machine can be expected to process a text of even moderate length by enumerating all possible disambiguations. A sentence containing $n$ scope bearing elements which are freely permutable will have $n!$ readings, if there are no other, say lexical or syntactic, sources of ambiguity. A series of $m$ such sentences would lead to $(n!)^m$ possibilities. All in all the growth of possibilities will be so fast that generating readings (...) first and testing their acceptability afterwards will not be feasible. -/- This insight has led a series of researchers to adopt a level of representation at which ambiguities remain unresolved. The idea here is not to generate and test many possible interpretations but to first generate one `underspecified' representation which in a sense represents all its complete specifications and then use whatever information is available to further specify the result. -/- One central hypothesis in the paper will be that the relation between an underspecified representation and its full representations is not so much the relation between one structure and a set of other structures but is in fact the relation between a description (a set of logical sentences) and its models. (shrink)