Gradability in Natural Language: Logical and Grammatical Foundations

This book presents a new theory of the relationship between vagueness, context-sensitivity, gradability, and scale structure in natural language. Heather Burnett argues that it is possible to distinguish between particular subclasses of adjectival predicates--relative adjectives like tall, total adjectives like dry, partial adjectives like wet, and non-scalar adjectives like hexagonal--on the basis of how their criteria of application vary depending on the context; how they display the characteristic properties of vague language; and what the properties of their associated orders are. It has been known for a long time that there exist empirical connections between context-sensitivity, vagueness, and scale structure; however, a formal system that expresses these connections had yet to be developed.

This volume sets out a new logical system, called DelTCS, that brings together insights from the Delineation Semantics framework and from the Tolerant, Classical, Strict non-classical framework, to arrive at a full theory of gradability and scale structure in the adjectival domain. The analysis is further extended to examine vagueness and gradability associated with particular classes of determiner phrases, showing that the correspondences that exist between the major adjectival scale structure classes and subclasses of determiner phrases can also be captured within the DelTCS system.

Heather Burnett is a CNRS researcher in the Laboratoire de Linguistique Formelle at l’Universite Paris 7-Denis Diderot. In 2012, she completed her PhD thesis in the Department of Linguistics at the University of California, Los Angeles under the supervision of Edward Keenan and Dominique Sportiche. From 2012-2014, she was a SSHRC postdoctoral fellow at l’Universite de Montreal; from 2014-2015, she was a CNRS postdoctoral researcher at l’Universite de Toulouse 2-Jean Jaures; and in 2015, she was a Banting postdoctoral fellow at the University of Toronto. Her work on formal semantics, formal syntax, and language variation and change has appeared in Linguistic Variation, Linguistics and Philosophy, and Journal of Semantics.