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

Thesis

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.

Authors: Worthing, D

• DOI: 10.5287/ora-wvbrjwjbe
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: degree semantics; Dependent Type Theory; spatial adjectives; compositionality; lexical networks
• Subjects: Formal semantics