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 ...

Coherence in conversations and in texts can be partially characterized by a set of coherence relations, motivated ultimately by the speaker's or writer's need to be understood. In this paper, formal definitions are given for several coherence relations, based on the operations of an inference system; that is, the relations between successive portions of a discourse are characterized in terms of the inferences that can be drawn from each. In analyzing a discourse, it is frequently the case that we would (...) recognize it as coherent, in that it would satisfy the formal definition of some coherence relation, if only we could assume certain noun phrases to be coreferential. In such cases, we will simply assume the identity of the entities referred to, in what might be called a “petty conversational implicature,” thereby solving the coherence and coreference problems simultaneously. Three examples of different kinds of reference problems are presented. In each, it is shown how the coherence of the discourse can be recognized, and how the reference problems are solved, almost as a by‐product, by means of these petty conversational implicatures. (shrink)

This book surveys the ways in which languages of different types refer to past, present, and future events and how these referents are related to the knowledge and attitudes of discourse participants. The book is the culmination of fifteen years of research by the author. Four major language types are examined in-depth: tense-based English, tense-aspect-based Polish, aspect-based Chinese, and mood-based Kalaallisut. Each contributes to a series of logical representation languages, which together define a common logical language that is argued to (...) underlie all language types. The four types differ in whether they choose to grammaticalize discourse reference to times (tense), events (aspect), and/or attitudes (mood), and how non-grammaticalized elements are inferred. The common logical language is a dynamic update logic, building on DRT and Centering Theory, but with a novel architecture—e.g. the distinction between focal vs. peripheral attention plays a key role, parallel to focal vs. peripheral vision. (shrink)

In this paper it is shown how the DRT (Discourse Representation Theory) treatment of temporal anaphora can be formalized within a version of Montague Semantics that is based on classical type logic.