This book studies formal semantics in modern type theories (MTT-semantics).
Compared with simple type theory, MTTs have much richer type structures and provide powerful means for adequate semantic constructions. This offers a serious alternative to the traditional set-theoretical foundation for linguistic semantics and opens up a new avenue for developing formal semantics that is both model-theoretic and proof-theoretic, which was not available before the development of MTT-semantics.
This book provides a reader-friendly and precise description of MTTs and offers a comprehensive introduction to MTT-semantics. It develops several case studies, such as adjectival modification and copredication, to exemplify the attractiveness of using MTTs for the study of linguistic meaning. It also examines existing proof assistant technology based on MTT-semantics for the verification of semantic constructions and reasoning in natural language. Several advanced topics are also briefly studied, including dependent event types, an application of dependent typing to event semantics.
1. Type Theories and Semantic Studies.
2. Modern Type Theories.
3. Formal Semantics in Modern Type Theories.
4. Advanced Modification.
5. Copredication and Individuation.
6. Reasoning and Verifying NL Semantics in Coq.
7. Advanced Topics.
Stergios Chatzikyriakidis is Associate Professor in Computational Linguistics and Associate Director of the Center for Linguistic Theory and Studies in Probability at the University of Gothenburg, Sweden. He is a computational semanticist with an interest in formal semantics and formal syntax.
Zhaohui Luo is Professor of Computer Science at Royal Holloway, University of London, UK. He has published extensively on type theory, including a research monograph published by Oxford University Press. His research has focused on MTT-semantics over the last decade.
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