Modern Perspectives in Type-Theoretical Semantics

1. Front Matter

   Pages i-viii

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2. Introduction: Modern Perspectives in Type Theoretical Semantics

   • Stergios Chatzikyriakidis, Zhaohui Luo

   Pages 1-8

3. Foundational Issues

   1. Front Matter

      Pages 9-9

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   2. Context-Passing and Underspecification in Dependent Type Semantics

      • Daisuke Bekki, Koji Mineshima

      Pages 11-41

   3. On the Interpretation of Common Nouns: Types Versus Predicates

      • Stergios Chatzikyriakidis, Zhaohui Luo

      Pages 43-70

   4. Adapting Type Theory with Records for Natural Language Semantics

      • Robin Cooper

      Pages 71-94

   5. Generalized Quantifiers on Dependent Types: A System for Anaphora

      • Justyna Grudzińska, Marek Zawadowski

      Pages 95-131

4. Types and Applications

   1. Front Matter

      Pages 133-133

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   2. Types, Meanings and Co-composition in Lexical Semantics

      • Nicholas Asher, Marta Abrusan, Tim Van de Cruys

      Pages 135-161

   3. Classifiers, Sorts, and Base Types in the Montagovian Generative Lexicon and Related Type Theoretical Frameworks for Lexical Compositional Semantics

      • Bruno Mery, Christian Retoré

      Pages 163-188

   4. Probabilistic Record Type Lattices for Incremental Reference Processing

      • Julian Hough, Matthew Purver

      Pages 189-222

   5. Intensions, Types and Finite-State Truthmaking

      • Tim Fernando

      Pages 223-243

5. Implementational Aspects

   1. Front Matter

      Pages 245-245

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   2. The Grail Theorem Prover: Type Theory for Syntax and Semantics

      • Richard Moot

      Pages 247-277

   3. Probability Distributions in Type Theory with Applications in Natural Language Syntax

      • Krasimir Angelov

      Pages 279-296

This book is a collective volume that reports the state of the art in the applications of type theory to linguistic semantics. The volume fills a 20 year gap from the last published book on the issue and aspires to bring researchers closer to cutting edge alternatives in formal semantics research. It consists of unpublished work by some key researchers on various issues related to the type theoretical study of formal semantics and further exemplifies the advantages of using modern type theoretical approaches to linguistic semantics. Themes that are covered include modern developments of type theories in formal semantics, foundational issues in linguistic semantics like anaphora, modality and plurals, innovational interdisciplinary research like the introduction of probability theory to type theories as well as computational implementations of type theoretical approaches. This volume will be of great interest to formal semanticists that are looking for alternative ways to study linguistic semantics, but will also be of interest to theoretical computer scientists and mathematicians that are interested in the applications of type theory.

• Anaphora
• Computation in natural language context
• Computational semantics
• Formal semantics
• Generalized Quantifiers on dependent types
• Grail theorem prover
• Lexical semantics
• Natural language semantics
• Type theory
• Type-logical grammars
• Unbound anaphora

“The papers of this collection illustrate how grammar-as-logic paradigms can be extended to match the rich expressivity of natural language, making use of Martin-Lӧf’s Type Theory, with its dramatically liberal concept of dependent typing. The authors vividly  demonstrate  the excitement of this research frontier, taking different sides in controversies such as:  whether the underlying form of explanation  should be semantic (model-theoretic) or syntactic (proof-theoretic);  how to model the shifting nature of lexical content within a formal grammar;  in what way such explanations should reflect the dynamics of language in use; with  due care  taken to  provide the  background needed for  the general reader to get a sense of   why these disputes remain of  foundational importance.  This volume is thus a must both for anyone interested in following current disputes in formal/computational linguistics, and for advanced linguistics students.” (Ruth Kempson, Emeritus Professor of Linguistics, King’s College London, UK)

• University of Gothenburg, Sweden & Open University Cyprus, Gothenburg, Sweden

  Stergios Chatzikyriakidis

• Dept. of Computer Science, University of London Royal Holloway, London, United Kingdom

  Zhaohui Luo

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