Compositional lexical networks: a case study of the English spatial adjectives

Most words cannot be given a single precise definition, but instead consist of multiple senses related to each other like members of a family. In cognitive approaches to semantics, this kind of category is described by a lexical, a diagram in which nodes represent senses and arrows represent sense connections. However, lexical network theory is not compositional: it does not explain how lexical networks are combined together to yield the meanings of phrases and sentences. The aim of this thesis is to develop lexical network theory in a formal, compositional setting. I argue that a traditional approach to formal semantics based on the simply-typed lambda calculus is not rich enough to implement lexical networks because it is unable to type the arrows which link word senses together. Instead, I propose replacing simple type theory with Martin-Löf Dependent Type Theory, and show how this allows for a fully compositional implementation of lexical networks. The resulting theory is applied to the description of the English spatial adjectives - high, low, tall, long, short, deep, shallow, thick and thin. These adjectives are an ideal starting point for studying the interaction between lexical and compositional semantics, since they have been studied extensively from both points of view. I illustrate how a compositional theory of lexical networks can provide an interface by which the insights of cognitive semantics can be imported into formal semantics, and vice versa

Parameterized monads in linguistics

A thesis submitted in partial fulfilment of the requirements of the University of Wolverhampton for the degree of Doctor of Philosophy.This dissertation follows the formal semantics approach to linguistics. It applies recent developments in computing theories to study theoretical linguistics in the area of the interaction between semantics and pragmatics and analyzes several natural language phenomena by parsing them in these theories. Specifically, this dissertation uses parameterized monads, a particular theoretical framework in category theory, as a dynamic semantic framework to reinterpret the compositional Discourse Representation Theory(cDRT), and to provide an analysis of donkey anaphora. Parameterized monads are also used in this dissertation to interpret information states as lists of presuppositions, and as dot types. Alternative interpretations for demonstratives and imperatives are produced, and the conventional implicature phenomenon in linguistics substantiated, using the framework. Interpreting donkey anaphora shows that parameterized monads is able to handle the sentential dependency. Therefore, this framework shows an expressive power equal to that of related frameworks such as the typed logical grammar and the dynamic predicate logic. Interpreting imperatives via parameterized monads also provides a compositional dynamic semantic analysis which is one of the main approaches to analysing imperatives