This book develops a theory of enriched meanings for natural language interpretation that uses the concept of monads and related ideas from category theory, a branch of mathematics that has been influential in theoretical computer science and elsewhere. Certain expressions that exhibit complex effects at the semantics/pragmatics boundary live in an enriched meaning space, while others live in a more basic meaning space. These basic meanings are mapped to enriched meanings only when required compositionally, which avoids generalizing meanings to the worst case. Ash Asudeh and Gianluca Giorgolo show that the monadic theory of enriched meanings offers a formally and computationally well-defined way to tackle important challenges at the semantics/pragmatics boundary. In particular, they develop innovative monadic analyses of three phenomena - conventional implicature, substitution puzzles, and conjunction fallacies - and demonstrate that the compositional properties of monads model linguistic intuitions about these cases particularly well. The analyses are accompanied by exercises to aid understanding, and the computational tools used are available on the book's companion website. The book also contains background chapters on enriched meanings and category theory. The volume is interdisciplinary in nature, with insights from semantics, pragmatics, philosophy of language, psychology, and computer science, and will appeal to graduate students and researchers from a wide range of disciplines with an interest in natural language understanding and representation.
Author(s): Ash Asudeh; Gianluca Giorgolo
Edition: Paperback
Publisher: Oxford University Press, USA
Year: 2020
Language: English
Pages: 192
Cover
Title Page
Copyright Page
Dedication Page
Table of Contents
General Preface
Acknowledgements
List of Figures
List of Tables
List of Symbols and Conventions
1. Introduction
1.1 Computational tool and exercises
PART I . BACKGROUND
2. Enriched meanings in semantics and pragmatics
2.1 Introduction
2.2 Semantics and pragmatics
2.3 Enriched meanings
2.4 The phenomena
2.4.1 Multidimensionality
2.4.2 Perspectives
2.4.3 Uncertainty
2.5 Conclusion
3. Category theory
3.1 Introduction
3.2 Categories
3.2.1 Category of linguistic meanings
3.3 Functors
3.4 Natural transformations
3.5 Monads
3.6 A logic for working with monads
3.7 Glue Semantics
3.8 Categorial Grammar
3.9 Exercises
PART II . CASE STUDIES
4.1 Introduction
4.2 Interdimensional backflow
4.3 Conventional implicatures and compositionality
4.4 A monad for conventional implicature
4.5 Analysis
4.5.1 Lexicon
4.5.2 Interpretation
4.6 Conclusion
4.7 Exercises
5. Perspectival reference
5.1 Introduction
5.2 The true scope of the problem
5.2.1 No embedding: simple sentences
5.2.2 Non-distinct terms: the Paderewski puzzle
5.2.3 Identity statements: delusions and mathematical truths
5.2.4 Summary: the space of possibilities
5.3 Formalization
5.3.1 A non-monadic formalization in Logical Form semantics
5.3.2 A monadic formalization
5.3.2.1 A monad for perspectives
5.3.2.2 Composition
5.4 Analysis
5.5 Previous approaches
5.6 Conclusion
5.7 Exercises
6. Uncertainty and conjunction fallacies
6.1 Introduction
6.2 Background
6.3 Monads and uncertainty
6.4 Conjunction fallacies, compositionally
6.5 One process, two representations
6.6 Analysis
6.7 Implications for the semantics/pragmatics boundary
6.7.1 Grice is nice?
6.7.2 Let’s get tropical
6.8 Conclusion
6.9 Exercises
PART III . COMPOSITION AND INTERACTIONS
7. Monad combinatorics
7.1 Introduction
7.2 Mixing phenomena
7.3 Distributive laws
7.4 Interpretation
7.5 Uncertainty
7.5.1 Uncertainty and conventional implicatures
7.5.2 Uncertainty and perspectives
7.6 Why do we need monads?
7.7 Conclusion
7.8 Exercises
7.9 Appendix A: Expanded terms
7.10 Appendix B: Natural deduction proofs
8. Conclusion
References
Author index
Subject index
