Introduction by Stergios Chatzikyriakidis and Zhaohui Luo -- Part I. Foundational Issues -- Context-Passing and Underspecification in Dependent Type Semantics by Daisuke Bekki and Koji Mineshima --  On the Interpretation of Common Nouns: Types v.s. Predicates by Stergios Chatzikyriakidis and Zhaohui Luo -- Adapting Type Theory with Records for Natural Language Semantics by Robin Cooper -- Generalized Quantifiers on Dependent Types: A System for Anaphora Language Semantics by Justyna Grudzińska and Marek Zawadowski -- Part II. Types and Applications -- Types, Meanings and Co-composition in Lexical Semantics by Nicholas Asher, Marta Abrusan and Tim van de Cruys -- Classifiers, Sorts, and Base Types in the Montagovian Generative Lexicon and Related Type Theoretical Frameworks for Lexical Compositional Semantics by Bruno Mery and Christian Retoré -- Probabilistic Record Type Lattices for Incremental Reference Processing by Julian Hough and Matthew Purver -- Intensions, Types and Finite-state Truthmaking by Tim Fernando -- Part III. Implementational Aspects -- The Grail Theorem Prover: Type theory for Syntax and Semantics by Richard Moot -- Probability Distributions in Type Theory with Applications in Natural Language Syntax by Krasimir Angelov.

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 It consists of unpublished work by some key researchers on various issues related to the type theoretical study of formal semantics and further exemplifies the advantages of using modern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.

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